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References

Published online by Cambridge University Press:  06 August 2022

Kiran S. Kedlaya
Kiran S. Kedlaya
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University of California, San Diego
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p-adic Differential Equations , pp. 469 - 488
Publisher: Cambridge University Press
Print publication year: 2022

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[1]Abbes, A. and Saito, T., Ramification of local fields with imperfect residue fields, Amer. J. Math. 124 (2002), 879–920.CrossRefGoogle Scholar
[2]Abbes, A. and Saito, T., Ramification of local fields with imperfect residue fields, II, Doc. Math. Extra Vol. (2003), 5–72.CrossRefGoogle Scholar
[3]Abbott, T.G., Kedlaya, K.S., and Roe, D., Bounding Picard numbers of surfaces using p-adic cohomology, in Arithmetic, Geometry and Coding Theory (AGCT 2005), Societé Mathématique de France, 2009, 125–159.Google Scholar
[4]Abe, T., Langlands correspondence for isocrystals and existence of crystalline companion for curves, J. Amer. Math. Soc. 31 (2018), 921–1057.CrossRefGoogle Scholar
[5]Abelard, S., Counting points on hyperelliptic curves in large characteristic: algorithms and complexity, thesis, Université de Lorraine, 2018, https://tel.archives-ouvertes.fr/tel-01876314.Google Scholar
[6]Abelard, S., Gaudry, P., and Spaenlehauer, P.-J., Improved complexity bounds for counting points on hyperelliptic curves, Found. Comp. Math. 19 (2019), 591–621. Google Scholar
[7]Abelard, S., Gaudry, P., and Spaenlehauer, P.-J., Counting points on genus-3 hyperelliptic curves with explicit real multiplication, in ANTS-XIII: Proceedings of the Thirteenth Algorithmic Number Theory Symposium, Open Book Series 2, Math. Sci. Pub., 2019, 1–19.Google Scholar
[8]Abramowitz, M. and Stegun, I.A., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables National Bureau of Standards Applied Math. Series 55, U.S. Government Printing Office, Washington, D.C., 1964.Google Scholar
[9]Adolphson, A., An index theorem for p-adic differential operators, Trans. Amer. Math. Soc. 216 (1976), 279–293.Google Scholar
[10]Adolphson, A. and Sperber, S., Exponential sums and Newton polyhedra: cohomology and estimates, Ann. of Math. 130 (1989), 367–406.Google Scholar
[11]Amini, O. and Baker, M., Linear series on metrized complexes of algebraic curves, Math. Ann. 362 (2015), 55–106.CrossRefGoogle Scholar
[12]Amini, O., Baker, M., Brugallé, E., and Rabinoff, J., Lifting harmonic morphisms I: metrized complexes and Berkovich skeleta, Res. Math. Sci. 2 (2015), 67pp.CrossRefGoogle Scholar
[13]Amini, O., Baker, M., Brugallé, E., and Rabinoff, J., Lifting harmonic morphisms II: Tropical curves and metrized complexes, Algebra and Number Theory 9 (2015), 267–315.Google Scholar
[14]Anderson, M. and Watkins, J., Coherence of power series rings over pseudo-Bezout domains, J. Alg. 107 (1987), 187–194.Google Scholar
[15]André, Y., Différentielles non commutatives et théorie de Galois différentielle ou aux différences, Ann. Sci. École Norm. Sup. (4) 34 (2001), 685–739.Google Scholar
[16]André, Y., Filtrations de type Hasse-Arf et monodromie p-adique, Invent. Math. 148 (2002), 285–317.Google Scholar
[17]André, Y., Dwork's conjecture on the logarithmic growth of solutions of p-adic differential equations, Compos. Math. 144 (2008), 484–494.Google Scholar
[18]André, Y., Slope filtrations, Confluentes Math. 1 (2009), 1–85.CrossRefGoogle Scholar
[19]André, Y., Baldassarri, F., and Cailotto, M., De Rham Cohomology of Differential Modules on Algebraic Varieties, second edition, Progress in Math. 189, Birkhäuser, 2020.Google Scholar
[20]André, Y. and Di Vizio, L., q-difference equations and p-adic local monodromy, Astérisque 296 (2004), 55–111.Google Scholar
[21]Arveson, W., An Invitation to C*-Algebras, Graduate Texts in Math. 39, Springer, 1976.CrossRefGoogle Scholar
[22]Asakura, M., An algorithm of computing special values of Dwork's p-adic hypergeometric functions in polynomial time, arXiv:1909.02700v3 (2019).Google Scholar
[23]Atiyah, M., Complex analytic connections in fibre bundles, Trans. Amer. Math. Soc. 85 (1957), 181–207.Google Scholar
[24]Atiyah, M.F. and Macdonald, I.G., Introduction to Commutative Algebra, Addison-Wesley, Reading, 1969.Google Scholar
[25]Auslander, M. and Goldman, O., Maximal orders, Trans. Amer. Math. Soc. 97 (1960), 1–24.Google Scholar
[26]Auslander, M. and Goldman, O., The Brauer group of a commutative ring, Trans. Amer. Math. Soc. 97 (1960), 367–409.Google Scholar
[27]Baker, M., An introduction to Berkovich analytic spaces and non-Archimedean potential theory on curves, in [360], 123–174.Google Scholar
[28]Baker, M., Payne, S., and Rabinoff, J., On the structure of non-Archimedean analytic curves, in Tropical and Non-Archimedean Geometry, Contemp. Math. 605, Amer. Math. Soc., Providence, 2013, 93–121.CrossRefGoogle Scholar
[29]Baker, M., Payne, S., and Rabinoff, J., Nonarchimedean geometry, tropicalization, and metrics on curves, Alg. Geom. 3 (2016), 63–105.Google Scholar
[30]Baker, M. and Rumely, R., Harmonic analysis on metrized graphs, Canad. J. Math. 59 (2007), 225–275.Google Scholar
[31]Baker, M. and Rumely, R., Potential Theory and Dynamics on the Berkovich Projective Line, Math. Surveys and Monographs 159, Amer. Math. Soc., 2010.CrossRefGoogle Scholar
[32]Baker, M. and Norine, S., Riemann-Roch and Abel-Jacobi theory on a finite graph, Adv. Math. 215 (2007), 766–788.Google Scholar
[33]Balakrishnan, J., Iterated Coleman integration for hyperelliptic curves, in ANTS-X: Proceedings of the Tenth Algorithmic Number Theory Symposium, Open Book Series 1, MSP, 2013, 41–61.Google Scholar
[34]Balakrishnan, J., Bradshaw, R., and Kedlaya, K.S., Explicit Coleman integration for hyperelliptic curves, in Algorithmic Number Theory (ANTS-IX), Lecture Notes in Comp. Sci. 6197, Springer-Verlag, 2010, 16–31.Google Scholar
[35]Balakrishnan, J. and Dogra, N., Quadratic Chabauty and rational points I: p-adic heights (with an appendix by J.S. Müller), Duke Math. J. 167 (2018), 1981–2038.Google Scholar
[36]Balakrishnan, J. and Dogra, N., Quadratic Chabauty and rational points II: Generalised height functions on Selmer varieties, Int. Math. Res. Notices 2020 (2020), article ID rnz362.Google Scholar
[37]Balakrishnan, J., Dogra, N., Müller, J.S., Tuitman, J., and Vonk, J., Explicit Chabauty-Kim for the split Cartan modular curve of level 13, Annals of Math. 189 (2019), 885–944.Google Scholar
[38]Balakrishnan, J. and Tuitman, J., Explicit Coleman integration for curves, Math. Comp. 89 (2020), 2965–2984.Google Scholar
[39]Baldassarri, F., Comparaison entre la cohomologie algébrique et la cohomologie p-adique rigide à coefficients dans un module différentiel. I. Cas des courbes, Invent. Math. 87 (1987), 83–99.Google Scholar
[40]Baldassarri, F., Comparaison entre la cohomology algébrique et la cohomologie p-adique rigide à coefficients dans un module différentiel. II. Cas des singularités régulières à plusieures variables, Math. Ann. 280 (1988), 417–439.Google Scholar
[41]Baldassarri, F., Continuity of the radius of convergence of differential equations on p-adic analytic curves, Invent. Math. 182 (2010), 513–584.Google Scholar
[42]Baldassarri, F. and Di Vizio, L., Continuity of the radius of convergence of p-adic differential equations on Berkovich analytic spaces, arXiv:0709.2008v3 (2008).Google Scholar
[43]Balser, W., Jurkat, W.B., and Lutz, D.A., Birkhoff invariants and Stokes’ multipliers for meromorphic linear differential equations, J. Math. Anal. Appl. 71 (1979), 48–94.Google Scholar
[44]Beilinson, A., Bloch, S., and Esnault, H., ϵ-factors for Gauss-Manin determinants, Moscow J. Math. 2 (2002), 477–532.Google Scholar
[45]Bellovin, R., p-adic Hodge theory in rigid analytic families, Algebra Number Theory 9 (2015), 371–433.Google Scholar
[46]Berger, L., Représentations p-adiques et équations différentielles, Invent. Math. 148 (2002), 219–284.CrossRefGoogle Scholar
[47]Berger, L., An introduction to the theory of p-adic representations, in Geometric Aspects of Dwork Theory. Vol I, II, de Gruyter, Berlin, 2004, 255–292.CrossRefGoogle Scholar
[48]Berger, L., Construction de (φ, Γ)-modules: représentations p-adiques et B-paires, Algebra and Num. Theory 2 (2008), 91–120.CrossRefGoogle Scholar
[49]Berger, L., Équations différentielles p-adiques et (φ, N)-modules filtrés, Astérisque 319 (2008), 13–38.Google Scholar
[50]Berger, L., Substitution maps in the Robba ring, arXiv:2012.01904v2 (2020).Google Scholar
[51]Berger, L. and Colmez, P., Familles de représentations de de Rham et monodromie p-adique, Astérisque 319 (2008), 303–337.Google Scholar
[52]Berkovich, V.G., Spectral Theory and Analytic Geometry over Non-Archimedean Fields, Math. Surveys and Monographs 33, Amer. Math. Soc., Providence, 1990.Google Scholar
[53]Berkovich, V.G., Étale cohomology for non-Archimedean analytic spaces, Publ. Math. IHÉS 78 (1993), 5–161.CrossRefGoogle Scholar
[54]Berkovich, V.G., Smooth p-adic analytic spaces are locally contractible, Invent. Math. 137 (1999), 1–84.Google Scholar
[55]Berkovich, V.G., Smooth p-adic analytic spaces are locally contractible, II, in Geometric Aspects of Dwork Theory, Vol. I, II, Walter de Gruyter, Berlin, 2004, 293–370.CrossRefGoogle Scholar
[56]Berthelot, P., Cohomologie Cristalline des Schémas de Caractéristique p > 0, Lecture Notes in Math. 407. Springer-Verlag, Berlin, 1974.Google Scholar
[57]Berthelot, P., Géométrie rigide et cohomologie des variétés algébriques de caractéristique p, Introductions aux cohomologies p-adiques (Luminy, 1984), Mém. Soc. Math. France (N.S.) 23 (1986), 7–32.Google Scholar
[58]Berthelot, P., Cohomologie rigide et cohomologie rigide à support propre. Première partie, Prépublication IRMAR 96-03, available at http://perso.univ-rennes1.fr/pierre.berthelot/ (retrieved June 2020).Google Scholar
[59]Berthelot, P., Finitude et pureté cohomologique en cohomologie rigide (with an appendix in English by A.J. de Jong), Invent. Math. 128 (1997), 329–377.CrossRefGoogle Scholar
[60]Berthelot, P., Dualité de Poincaré et formule de Künneth en cohomologie rigide, C.R. Acad. Sci. Paris 325 (1997), 493–498.CrossRefGoogle Scholar
[61]Berthelot, P., Introduction à la théorie arithmétique des 𝒟-modules, Cohomologies p-adiques et applications arithmétiques, II, Astérisque 279 (2002), 1–80.Google Scholar
[62]Berthelot, P. and Ogus, A., Notes on Crystalline Cohomology, Princeton University Press, Princeton, 1978.Google Scholar
[63]Bhatia, R., Matrix Analysis, Graduate Texts in Math. 169, Springer-Verlag, New York, 1997.Google Scholar
[64]Bhatt, B. and Scholze, P., Prisms and prismatic cohomology, arXiv:1905.08229v2 (2019).Google Scholar
[65]Bojković, V., Riemann-Hurwitz formula for finite morphisms of p-adic curves, Math. Z. 288 (2018), 1165–1193.Google Scholar
[66]Bojković, V. and Poineau, J., On the number of connected components of the ramification locus of a morphism of Berkovich curves, Math. Ann. 372 (2018), 1575–1595.Google Scholar
[67]Borger, J.M., Conductors and the moduli of residual perfection, Math. Annalen 329 (2004), 1–30.Google Scholar
[68]Bosch, S., Lectures on Formal and Rigid Geometry, Lecture Notes in Math. 2105, Springer, Cham, 2014.CrossRefGoogle Scholar
[69]Bosch, S., Güntzer, U., and Remmert, R., Non-Archimedean Analysis, Grundlehren der Math. Wiss. 261, Springer-Verlag, Berlin, 1984.Google Scholar
[70]Brezner, U. and Temkin, M., Lifting problem for minimally wild covers of Berkovich curves, J. Alg. Geom. 29 (2020), 123–166.Google Scholar
[71]Brinon, O. and Conrad, B., p-adic Hodge theory, notes from the 2009 Clay Mathematics Institute summer school, available online at https://math.stanford.edu/~conrad/ (retrieved June 2020).Google Scholar
[72]Boucksom, S., Favre, C., and Jonsson, M., Valuations and plurisubharmonic singularities, Publ. Res. Inst. Math. Sci. 44 (2008), 449–494.Google Scholar
[73]Buium, A., Differential characters of abelian varieties over p-adic fields, Invent. Math. 122 (1995), 309–340.Google Scholar
[74]Buium, A., Arithmetic analogues of derivations, J. Algebra 198 (1997), 290–299.CrossRefGoogle Scholar
[75]Buzzard, K. and Calegari, F., Slopes of overconvergent 2-adic modular forms, Compos. Math. 141 (2005), 591–604.Google Scholar
[76]Cais, B. (ed.), Perfectoid Spaces: Lectures from the 2017 Arizona Winter School, Math. Surveys and Monographs 242, Amer. Math. Soc., 2019, 58–205.Google Scholar
[77]Caro, D., F-isocristaux surconvergents et surcohérence différentielle, Invent. Math. 170 (2007), 507–539.Google Scholar
[78]Caro, D., Dévissages des F-complexes de 𝒟-modules arithmétiques en F-isocristaux surconvergents, Invent. Math. 166 (2006), 397–456.Google Scholar
[79]Carothers, N.L., A Short Course on Banach Space Theory, Cambridge University Press, Cambridge, 2004.CrossRefGoogle Scholar
[80]Caruso, X., Roe, D., and Vaccon, T., p-adic stability in linear algebra, in ISSAC’15— Proceedings of the 2015 ACM International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2015, 101–108.Google Scholar
[81]Caruso, X., Roe, D., and Vaccon, T., Characteristic polynomials of p-adic matrices, in ISSAC’17—Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation, ACM, New York, 2017, 389–396.Google Scholar
[82]Cassels, J.W.S., Local Fields, London Math. Society Student Texts 3, Cambridge University Press, Cambridge, 1986.Google Scholar
[83]Castryck, W. and Tuitman, J., Point counting on curves using a gonality preserving lift, Quart. J. Math. 69 (2018), 33–74.Google Scholar
[84]Cherbonnier, F. and Colmez, P., Représentations p-adiques surconvergentes, Invent. Math. 133 (1998), 581–611.Google Scholar
[85]Chiarellotto, B. and Christol, G., On overconvergent isocrystals and F-isocrystals of rank one. Compos. Math. 100 (1996), 77–99.Google Scholar
[86]Chiarellotto, B. and Pulita, A., Arithmetic and Differential Swan conductors of rank one representations with finite local monodromy, Amer. J. Math. 131 (2009), no. 6, 1743–1794.Google Scholar
[87]Chiarellotto, B. and Tsuzuki, N., Logarithmic growth and Frobenius filtrations for solutions of p-adic differential equations, J. Inst. Math. Jussieu 8 (2009), 465–505.Google Scholar
[88]Chiarellotto, B. and Tsuzuki, N., Log-growth filtration and Frobenius slope filtration of F-isocrystals at the generic and special points, Doc. Math. 16 (2011), 33–69.Google Scholar
[89]Christol, G., Modules Différentiels et Equations Différentielles p-adiques, Queen's Papers in Pure and Applied Math. 66, Queen's University, Kingston, 1983.Google Scholar
[90]Christol, G., Un théorème de transfert pour les disques singuliers réguliers, Cohomologie p-adique, Astérisque 119–120 (1984), 151–168.Google Scholar
[91]Christol, G., About a Tsuzuki theorem, in p-adic Functional Analysis (Ioannina, 2000), Lecture Notes in Pure and Appl. Math., 222, Dekker, New York, 2001, 63–74.Google Scholar
[92]Christol, G., Thirty years later, in Geometric Aspects of Dwork Theory (Volume I), de Gruyter, Berlin, 2004, 419–436.Google Scholar
[93]Christol, G., Le Théorème de Turritin p-adique, manuscript available at https://webusers.imj-prg.fr/~gilles.christol/courspdf.pdf (retrieved July 2020).Google Scholar
[94]Christol, G. and Dwork, B., Effective p-adic bounds at regular singular points, Duke Math. J. 62 (1991), 689–720.Google Scholar
[95]Christol, G. and Dwork, B., Differential modules of bounded spectral norm, in p-adic Methods in Number Theory and Algebraic Geometry, Contemp. Math. 133, Amer. Math. Soc., Providence, 1992.Google Scholar
[96]Christol, G. and Dwork, B., Modules différentielles sur les couronnes, Ann. Inst. Fourier 44 (1994), 663–701.CrossRefGoogle Scholar
[97]Christol, G. and Mebkhout, Z., Sur le théorème de l’indice des équations différentielles p-adiques, Annals de l’Institut Fourier 43 (1993), 1545–1574.Google Scholar
[98]Christol, G. and Mebkhout, Z., Sur le théorème de l’indice des équations différentielles p-adiques II, Annals of Math. 146 (1997), 345–410.Google Scholar
[99]Christol, G. and Mebkhout, Z., Sur le théorème de l’indice des équations différentielles p-adiques III, Annals of Math. 151 (2000), 385–457.CrossRefGoogle Scholar
[100]Christol, G. and Mebkhout, Z., Sur le théorème de l’indice des équations différentielles p-adiques IV, Invent. Math. 143 (2001), 629–672.Google Scholar
[101]Churchill, R.C. and Kovacic, J.J., Cyclic vectors, in Differential Algebra and Related Topics (Newark, NJ, 2000), World Scientific, River Edge, NJ, 2002, 191–218.Google Scholar
[102]Clark, D., A note on the p-adic convergence of solutions of linear differential equations, Proc. Amer. Math. Soc. 17 (1966), 262–269.Google Scholar
[103]Cohen, H. and Frey, G. (eds.), Handbook of Elliptic and Hyperelliptic Curve Cryptography, Discrete Math. and its Applications 34, Chapman & Hall/CRC, 2005.CrossRefGoogle Scholar
[104]Cohen, A., Temkin, M., and Trushin, D., Morphisms of Berkovich curves and the different function, Adv. Math. 303 (2016), 800–858.Google Scholar
[105]Cohn, R.M., Difference Algebra, John Wiley & Sons, New York, London, Sydney, 1965.Google Scholar
[106]Coleman, R.F., Dilogarithms, regulators and p-adic L-functions, Invent. Math. 69 (1982), 171–208.CrossRefGoogle Scholar
[107]Coleman, R.F., Torsion points on curves and p-adic abelian integrals, Ann. of Math. 121 (1985), 111–168.Google Scholar
[108]Coleman, R.F., Effective Chabauty, Duke Math. J. 52 (1985), 765–770.Google Scholar
[109]Collins, M., On Jordan's theorem for complex linear groups, J. Group Theory 10 (2007), 411–423.CrossRefGoogle Scholar
[110]Colmez, P., Représentations triangulines de dimension 2, Astérisque 319 (2008), 213–258.Google Scholar
[111]Conrad, B., Several approaches to non-archimedean geometry, in [360], 24–79.Google Scholar
[112]Conrad, B., Relative ampleness in rigid geometry, Ann. Inst. Fourier 56 (2006), 1049–1126.Google Scholar
[113]Cope, F.T., Formal solutions of irregular linear differential equations, II, Amer. J. Math. 58 (1936), 130–140.Google Scholar
[114]Costa, E., Harvey, D., and Kedlaya, K.S., Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in p-adic cohomology, in ANTS XIII: Proceedings of the Thirteenth Algorithmic Number Theory Symposium, Open Book Series 2, Math. Sci. Pub., Berkeley, 2019, 221–238.Google Scholar
[115]Costa, E., Kedlaya, K.S., and Roe, D., Hypergeometric L-functions in average polynomial time, in ANTS-XIV: Proceedings of the Fourteenth Algorithmic Number Theory Symposium, Open Book Series 4, Math. Sci. Pub., Berkeley, 2020, 143–159.Google Scholar
[116]Costa, E. and Sertöz, E.C., Effective obstruction to lifting Tate classes from positive characteristic, arXiv:2003.11037v1 (2020).Google Scholar
[117]Crew, R., F-isocrystals and p-adic representations, in Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Proc. Sympos. Pure Math., 46, Part 2, Amer. Math. Soc., Providence, 1987, 111–138.Google Scholar
[118]Crew, R., Finiteness theorems for the cohomology of an overconvergent isocrystal on a curve, Ann. Sci. Éc. Norm. Sup. 31 (1998), 717–763.Google Scholar
[119]Crew, R., Canonical extensions, irregularities, and the Swan conductor, Math. Ann. 316 (2000), 19–37.Google Scholar
[120]Csima, N.E., Newton-Hodge filtration for self-dual F-crystals, Math. Nachr. 284 (2011), 1394–1403.Google Scholar
[121]Curtis, C.W. and Reiner, I., Representation Theory of Finite Groups and Associative Algebras, reprint of the 1962 original, Amer. Math. Soc., Providence, 2006.CrossRefGoogle Scholar
[122]D’Agnolo, A., and Kashiwara, M., Riemann-Hilbert correspondence for holonomic D-modules, Publ. Math. IHÉS 123 (2016), 69–197.Google Scholar
[123]de Jong, A.J., Homomorphisms of Barsotti-Tate groups and crystals in positive characteristic, Invent. Math. 134 (1998), 301–333; erratum, ibid. 138 (1999), 225.Google Scholar
[124]de Jong, A.J., Barsotti-Tate groups and crystals, Proceedings of the International Congress of Mathematicians, Vol. II (Berlin, 1998), Doc. Math. Extra Vol. II (1998), 259–265.Google Scholar
[125]de Jong, A.J. and Oort, F., Purity of the stratification by Newton polygons, J. Amer. Math. Soc. 13 (2000), 209–241.Google Scholar
[126]Deligne, P., Équations Différentielles à Points Singuliers Réguliers, Lecture Notes in Math. 163, Springer-Verlag, Berlin, 1970.Google Scholar
[127]Deligne, P., Catégories tannakiennes, in The Grothendieck Festschrift, volume II, Birkhäuser, Boston, 1990, 111–195.Google Scholar
[128]Deligne, P., La conjecture de Weil, II, Publ. Math. IHÉS 52 (1980), 137–252.Google Scholar
[129]Deligne, P. and Katz, N. (eds.), Groupes de Monodromie en Géométrie Algébrique II, Séminaire de Géométrie Algébrique du Bois-Marie 1967–1969 (SGA 7 II), Lecture Notes in Math. 340, Springer-Verlag, Berlin-New York, 1973.Google Scholar
[130]Deligne, P. and Milne, J.S., Tannakian categories, in Hodge Cycles, Motives and Shimura Varieties, Lecture Notes in Math. 900, Springer-Verlag, Berlin, 1982.Google Scholar
[131]Demazure, M., Lectures on p-divisible Groups, Lecture Notes in Math. 302, Springer-Verlag, New York, 1972.Google Scholar
[132]Denef, J. and Vercauteren, F., An extension of Kedlaya's algorithm to hyperelliptic curves in characteristic 2, J. Cryptology 19 (2006), 1–25.Google Scholar
[133]Di Vizio, L., Local analytic classification of q-difference equations with |q| = 1, J. Noncommutative Geom. 3 (2009), 125–149.Google Scholar
[134]Dokchitser, T., Dokchitser, V., Maistret, C., and Morgan, A., Semistable types of hyperelliptic curves, in Algebraic Curves and their Applications, Contemp Math. 724, Amer. Math. Soc., Providence, 2019, 73–135.Google Scholar
[135]Dokchitser, T., Dokchister, V., Maistret, C., and Morgan, A., Arithmetic of hyperelliptic curves over local fields, arXiv:1808.02936v2 (2018).Google Scholar
[136]Drinfeld, V.G., Langlands’ Conjecture for GL(2) over functional Fields, Proceedings of the International Congress of Mathematicians, Helsinki, 565–574 (1978).Google Scholar
[137]Ducros, A., La Structure des Courbes Analytiques, manuscript available at https://webusers.imj-prg.fr/~antoine.ducros/livre.html (retrieved June 2021).Google Scholar
[138]Dwork, B., On the rationality of the zeta function of an algebraic variety, Amer. J. Math. 82 (1960), 631–648.Google Scholar
[139]Dwork, B., On the zeta function of a hypersurface, Publ. Math. IHÉS 12 (1962), 5–68.Google Scholar
[140]Dwork, B., p-adic cycles, Publ. Math. IHÉS 37 (1969), 27–115.Google Scholar
[141]Dwork, B., On p-adic differential equations, II. The p-adic asymptotic behavior of solutions of ordinary linear differential equations with rational function coefficients, Ann. of Math. (2) 98 (1973), 366–376.Google Scholar
[142]Dwork, B., On p-adic differential equations, III. On p-adically bounded solutions of ordinary linear differential equations with rational function coefficients, Invent. Math. 20 (1973), 35–45.Google Scholar
[143]Dwork, B., On p-adic differential equations. IV. Generalized hypergeometric functions as p-adic analytic functions in one variable. Ann. Sci. Éc. Norm. Sup. 6 (1973), 295–315.Google Scholar
[144]Dwork, B., Bessel functions as p-adic functions of the argument, Duke Math. J. 41 (1974), 711–738.Google Scholar
[145]Dwork, B., Lectures on p-adic Differential Equations, Grundlehren der math. Wissenschaften 253, Springer-Verlag, New York, 1982.Google Scholar
[146]Dwork, B., On the uniqueness of Frobenus operator on differential equations, in Algebraic Number Theory, Adv. Stud. Pure Math. 17, Academic Press, Boston, MA, 1989, 89–96.Google Scholar
[147]Dwork, B., Generalized Hypergeometric Functions, Clarendon Press, Oxford, 1990.Google Scholar
[148]Dwork, B.M., On exponents of p-adic differential modules, J. reine angew. Math. 484 (1997), 85–126.Google Scholar
[149]Dwork, B., Gerotto, G., and Sullivan, F., An Introduction to G-Functions, Annals of Math. Studies 133, Princeton University Press, Princeton, 1994.Google Scholar
[150]Dwork, B. and Robba, P., On ordinary linear p-adic differential equations, Trans. Amer. Math. Soc. 231 (1977), 1–46.Google Scholar
[151]Dwork, B. and Robba, P., Effective p-adic bounds for solutions of homogeneous linear differential equations, Trans. Amer. Math. Soc. 259 (1980), 559–577.Google Scholar
[152]Edixhoven, B., Point counting after Kedlaya, course notes (2006) available at https://www.math.leidenuniv.nl/~edix/oww/mathofcrypt/carls_edixhoven/kedlaya.pdf (retrieved June 2020).Google Scholar
[153]Edixhoven, B. and Lido, G., Geometric quadratic Chabauty, arXiv:1910.10752v3 (2020).Google Scholar
[154]Eisenbud, D., Commutative Algebra with a View Toward Algebraic Geometry, Graduate Texts in Math. 150, Springer-Verlag, New York, 1995.Google Scholar
[155]Elsenhans, A.-S. and Jahnel, J., Point counting on K3 surfaces and an application concerning real and complex multiplication, LMS J. Comput. Math. 19 (2016), 12–28.Google Scholar
[156]Enflo, P., A counterexample to the approximation problem in Banach spaces, Acta Math. 130 (1973), 309–317.Google Scholar
[157]Escassut, A., Algèbres d’éléments analytiques en analyse non archimedienne, Indag. Math. 77 (1974), 339–351.CrossRefGoogle Scholar
[158]Faber, X., Topology and geometry of the Berkovich ramification locus for rational functions, I, Manuscripta Math. 142 (2013), 439–474.Google Scholar
[159]Faber, X., Topology and geometry of the Berkovich ramification locus for rational functions, II, Math. Ann. 356 (2013), 819–844.Google Scholar
[160]Fargues, L. and Fontaine, J.-M., Courbes et fibrés vectoriels en théorie de Hodge p-adique, Astérisque 406 (2018).Google Scholar
[161]Fargues, L. and Scholze, P., Geometrization of the local Langlands correspondence, arXiv:arXiv:2102.13459v2 (2021).Google Scholar
[162]Faltings, G., Coverings of p-adic period domains, research announcement (2007) available at http://www.mpim-bonn.mpg.de/preprints/ (retrieved June 2020).Google Scholar
[163]Favre, C. and Jonsson, M., The Valuative Tree, Lecture Notes in Math. 1853, Springer-Verlag, Berlin, 2004.Google Scholar
[164]Favre, C. and Jonsson, M., Valuations and multiplier ideals, J. Amer. Math. Soc. 18 (2005), 655–684.Google Scholar
[165]Fontaine, J.-M., Représentations p-adiques des corps locaux, I, in The Grothendieck Festschrift, Vol. II, Progress in Math. 87, Birkhäuser, Boston, 1990, 249–309.Google Scholar
[166]Fontaine, J.-M., Représentations p-adiques semi-stables, Périodes p-adiques (Bures-sur-Yvette, 1988), Astérisque 23 (1994), 113–184.Google Scholar
[167]Fontaine, J.-M., Représentations de de Rham et représentations semi-stables, Orsay preprint number 2004-12, available online at https://www.imo.universite-paris-saclay.fr/~biblio/pub/2004/ (retrieved June 2020).Google Scholar
[168] Fontaine, J.-M. and Ouyang, Y., Theory of p-adic Galois Representations, available online at http://staff.ustc.edu.cn/~yiouyang/ (retrieved July 2020).Google Scholar
[169]Fontaine, J.-M. and Wintenberger, J.-P., Le “corps de normes” de certaines extensions algébriques de corps locaux, C.R. Acad. Sci. Paris Sér. A-B 288 (1979), A367–A370.Google Scholar
[170]Fresnel, J. and Matignon, M., Produit tensoriel topologique de corps valués, Canad. J. Math. 35 (1983), 218–273.Google Scholar
[171]Fresnel, J. and van der Put, M., Rigid Analytic Geometry and its Applications, Progress in Mathematics 218, Birkhäuser, Boston, 2004.Google Scholar
[172]Fulton, W., Intersection Theory, second edition, Springer-Verlag, Berlin, 1998.Google Scholar
[173]Fulton, W., Eigenvalues, invariant factors, highest weights, and Schubert calculus, Bull. Amer. Math. Soc. (N.S.) 37 (2000), 209–249.Google Scholar
[174]Gaudry, P. and Schost, É., Genus 2 point counting over prime fields, J. Symb. Comp. 47 (2012), 368–400.Google Scholar
[175]Gelfand, I.M., Kapranov, M.M., and Zelevinsky, A.V., Discriminants, Resultants and Multidimensional Determinants, reprint of the 1994 edition, Birkhäuser, Boston, 2008.Google Scholar
[176]Gérard, R. and Levelt, A.M., Invariants mesurant l’irrégularité en un point singulier des systèmes d’équations différentielles linéaires, Ann. Inst. Fourier (Grenoble) 23 (1973), 157–195.Google Scholar
[177]Gerkmann, R., Relative rigid cohomology and deformation of hypersurfaces, Int. Math. Res. Papers 2007 (2007), article ID rpm003 (67 pages).Google Scholar
[178]Gouvêa, F.Q., p-adic Numbers: An Introduction, third edition, Universitext 223, Springer, Cham, 2020.Google Scholar
[179]Griffiths, P. and Harris, J., Principles of Algebraic Geometry, Wiley Interscience, New York, 1978.Google Scholar
[180]Grothendieck, A., La théorie de Fredholm, Bull. Soc. Math. France 84 (1956), 319–384.Google Scholar
[181]Grothendieck, A., Sur la classification des fibrés holomorphes sur la sphère de Riemann, Amer. J. Math. 79 (1957), 121–138.Google Scholar
[182]Grothendieck, A., On the de Rham cohomology of algebraic varieties, Publ. Math. IHÉS 29 (1966), 95–103.Google Scholar
[183]Grothendieck, A., Revêtements Étales et Groupe Fondamental, Séminaire de Géométrie Algébrique du Bois-Marie 1960–1961 (SGA 1), Lecture Notes in Math. 224, Springer-Verlag, Berlin, 1971.Google Scholar
[184]Grothendieck, A., Le groupe de Brauer: I. Algébres d’Azumaya et interprétations diverses, in Séminaire Bourbaki, Vol. 9, Exposé 290, Soc. Math. France, Paris, 1995, 199–219.Google Scholar
[185]Gubler, W., Rabinoff, J., and Werner, A., Skeletons and tropicalizations, Adv. Math. 294 (2016), 150–215.Google Scholar
[186]Gubler, W., Rabinoff, J., and Werner, A., Tropical skeletons, Ann. Inst. Fourier, Grenoble 67 (2017), 1905–1961.Google Scholar
[187]Guennebaud, B., Sur une notion de spectre pour les algébres normées ultramétriques, PhD thesis, Université de Poitiers, 1973; available at http://www.ihes.fr/~gabber/GUENN.pdf (retrieved April 2017).Google Scholar
[188]Guralnick, R.M. and Lorenz, M., Orders of finite groups of matrices, in Groups, Rings and Algebras, Contemp. Math. 420, Amer. Math. Soc., Providence, 2006, 141–161.Google Scholar
[189]Hahn, H., Über die nichtarchimedische Größensysteme, in Gesammelte Abhandlungen I, Springer, Vienna, 1995.Google Scholar
[190]Hartl, U., Period spaces for Hodge structures in equal characteristic, Annals of Math. 173 (2011), 1241–1358.Google Scholar
[191]Hartl, U., On a conjecture of Rapoport and Zink, Invent. Math. 193 (2013), 627–696.Google Scholar
[192]Hartl, U., On period spaces for p-divisible groups, C.R. Math. Acad. Sci. Paris 346 (2008), 1123–1128.Google Scholar
[193]Hartl, U. and Pink, R., Vector bundles with a Frobenius structure on the punctured unit disc, Compos. Math. 140 (2004), 689–716.Google Scholar
[194]Hartshorne, R., Residues and Duality, Lecture Notes in Math. 20, Springer, New York, 1966.Google Scholar
[195]Hartshorne, R., On the de Rham cohomology of algebraic varieties, Publ. Math. IHÉS 45 (1975), 5–99.Google Scholar
[196]Hartshorne, R., Algebraic Geometry, Graduate Texts in Math. 52, Springer-Verlag, New York, 1977.Google Scholar
[197]Harvey, D., Kedlaya's algorithm in larger characteristic, Int. Math. Res. Notices 2007 (2007), article ID rnm095 (29 pages).Google Scholar
[198]Harvey, D., Computing zeta functions of arithmetic schemes, Proc. London Math. Soc. 111 (2015), 1379–1401.Google Scholar
[199]Hazewinkel, M., Gauss-Manin connection, entry in Encyclopedia of Mathematics, third edition, Kluwer, 2001; available online at https://encyclopediaofmath.org/wiki/Gauss-Manin_connection.Google Scholar
[200]Hazewinkel, M., Witt vectors, I, in Handbook of Algebra. Vol. 6, Handb. Algebr. 6, Elsevier/North-Holland, Amsterdam, 2009, 319–472.CrossRefGoogle Scholar
[201]Herr, L., Sur la cohomologie galoisienne des corps p-adiques, Bull. Soc. Math. France 126 (1998), 563–600.Google Scholar
[202]Herr, L., Une approche nouvelle de la dualité locale de Tate, Math. Ann. 320 (2001), 307–337.Google Scholar
[203]Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic zero: I, Annals of Math. 79 (1964), 109–203.Google Scholar
[204]Hironaka, H., Resolution of singularities of an algebraic variety over a field of characteristic zero: II, Annals of Math. 79 (1964), 205–326.Google Scholar
[205]Hodge, W.V.D. and Pedoe, D., Methods of Algebraic Geometry, Vol. III (reprint of the 1954 original), Cambridge University Press, Cambridge, 1994.Google Scholar
[206]Hoobler, R.T., The differential Brauer group, arXiv:1003.1421v1 (2010).Google Scholar
[207]Horn, A., On the eigenvalues of a matrix with prescribed singular values, Proc. Amer. Math. Soc. 5 (1954), 4–7.Google Scholar
[208]Horn, A., Eigenvalues of sums of Hermitian matrices, Pacific J. Math. 12 (1962), 225–241.Google Scholar
[209]Horn, R.A. and Johnson, C.R., Topics in Matrix Analysis, Cambridge Univ. Press, Cambridge, 2011.Google Scholar
[210]Hrushovski, E., Loeser, F., and Poonen, B., Berkovich spaces embed in Euclidean spaces, Enseign. Math. 60 (2014), 273–292.Google Scholar
[211]Huber, R., A generalization of formal schemes and rigid analytic varieties, Math. Z. 217 (1994), 513–551.Google Scholar
[212]Huber, R., Étale Cohomology of Rigid Analytic Varieties and Adic Spaces, Aspects of Math., Springer, Wiesbaden, 1996.Google Scholar
[213]Huber, R., Swan representations associated with rigid analytic curves, J. reine angew. Math. 537 (2001), 165–234.Google Scholar
[214]Hubrechts, H., Point counting in families of hyperelliptic curves, Found. Comp. Math. 8 (2008), 137–169.Google Scholar
[215]Hubrechts, H., Memory efficient hyperelliptic curve point counting, Int. J. Number Theory 7 (2011), 203–214.Google Scholar
[216]Illusie, L., Crystalline cohomology, in Motives (Seattle, WA, 1991), Proc. Sympos. Pure Math., 55, Part 1, Amer. Math. Soc., Providence, 1994, 43–70.Google Scholar
[217]Jacobson, N., Basic Algebra I, second edition, W.H. Freeman, New York, 1985.Google Scholar
[218]Joyal, A., δ-anneau et vecteurs de Witt, C.R. Math. Rep. Acad. Sci. Canada 7 (1985), 177–182.Google Scholar
[219]Joyal, A., δ-anneau et λ-anneaux, II, C.R. Math. Rep. Acad. Sci. Canada 7 (1985), 227–232.Google Scholar
[220]Kajiwara, T., Tropical toric geometry, in Toric Topology, Contemp. Math. 460, Amer. Math. Soc., Providence, 2008, 197–207.Google Scholar
[221]Kaplansky, I., Maximal fields with valuations, Duke Math. J. 9 (1942), 303–321.Google Scholar
[222]Kato, K., Swan conductors for characters of degree one in the imperfect residue field case, in Algebraic K-theory and algebraic number theory (Honolulu, HI, 1987), Contemp. Math. 83, Amer. Math. Soc., Providence, 1989, 101–131.CrossRefGoogle Scholar
[223]Katz, N.M., Nilpotent connections and the monodromy theorem: applications of a result of Turrittin, Publ. Math. IHÉS 39 (1970), 175–232.Google Scholar
[224]Katz, N.M., Slope filtration of F-crystals, Journées de Géométrie Algébrique de Rennes (Rennes, 1978), Vol. I, Astérisque 63 (1979), 113–163.Google Scholar
[225]Katz, N.M., Local-to-global extensions of representations of fundamental groups, Ann. Inst. Fourier (Grenoble) 36 (1986), 69–106.Google Scholar
[226]Katz, N.M., On the calculation of some differential Galois groups, Invent. Math. 87 (1987), 13–61.Google Scholar
[227]Katz, N.M., A simple algorithm for cyclic vectors, Amer. J. Math. 109 (1987), 65–70.Google Scholar
[228]Katz, N.M. and Oda, T., On the differentiation of de Rham cohomology classes with respect to parameters, J. Math. Kyoto Univ. 8 (1968), 199–213.Google Scholar
[229]Kedlaya, K.S., Counting points on hyperelliptic curves using Monsky-Washnitzer cohomology, J. Ramanujan Math. Soc. 16 (2001), 323–338; errata, ibid. 18 (2003), 417–418.Google Scholar
[230]Kedlaya, K.S., A p-adic local monodromy theorem, Annals of Math. 160 (2004), 93–184.Google Scholar
[231]Kedlaya, K.S., Full faithfulness for overconvergent F-isocrystals, in Geometric Aspects of Dwork Theory (Volume II), de Gruyter, Berlin, 2004, 819–835.Google Scholar
[232]Kedlaya, K.S., Computing zeta functions via p-adic cohomology, Algorithmic Number Theory (ANTS VI), Lecture Notes in Comp. Sci. 3076, Springer-Verlag, 2004, 1–17.Google Scholar
[233]Kedlaya, K.S., Local monodromy of p-adic differential equations: an overview, Int. J. Number Theory 1 (2005), 109–154; errata at https://kskedlaya.org/papers/.Google Scholar
[234]Kedlaya, K.S., Slope filtrations revisited, Documenta Math. 10 (2005), 447–525; errata, ibid. 12 (2007), 361–362.Google Scholar
[235]Kedlaya, K.S., Frobenius modules and de Jong's theorem, Math. Res. Lett. 12 (2005), 303–320; errata at https://kskedlaya.org/papers/.Google Scholar
[236]Kedlaya, K.S., Finiteness of rigid cohomology with coefficients, Duke Math. J. 134 (2006), 15–97.Google Scholar
[237]Kedlaya, K.S., Fourier transforms and p-adic “Weil II”, Compos. Math. 142(2006), 1426–1450.Google Scholar
[238]Kedlaya, K.S., Swan conductors for p-adic differential modules, I: A local construction, Algebra and Number Theory 1 (2007), 269–300.Google Scholar
[239]Kedlaya, K.S., Semistable reduction for overconvergent F-isocrystals, I: Unipotence and logarithmic extensions, Compos. Math. 143 (2007), 1164–1212.Google Scholar
[240]Kedlaya, K.S., The p-adic local monodromy theorem for fake annuli, Rend. Sem. Math. Padova 118 (2007), 101–146.Google Scholar
[241]Kedlaya, K.S., Slope filtrations for relative Frobenius, Astérisque 319 (2008), 259–301.Google Scholar
[242]Kedlaya, K.S., Semistable reduction for overconvergent F-isocrystals, II: A valuation-theoretic approach, Compos. Math. 144 (2008), 657–672.Google Scholar
[243]Kedlaya, K.S., p-adic cohomology: from theory to practice, in [360], 190–219.Google Scholar
[244]Kedlaya, K.S., Effective p-adic cohomology for cyclic cubic threefolds, in Computational Algebraic and Analytic Geometry, Contemp. Math. 572, Amer. Math. Soc., 127–171.Google Scholar
[245]Kedlaya, K.S., Semistable reduction for overconvergent F-isocrystals, III: Local semistable reduction at monomial valuations, Compos. Math. 145 (2009), 143–172.Google Scholar
[246]Kedlaya, K.S., p-adic cohomology, in Algebraic Geometry: Seattle 2005, Proc. Symp. Pure Math. 80, Amer. Math. Soc., 2009, 667–684.Google Scholar
[247]Kedlaya, K.S., Some new directions in p-adic Hodge theory, J. Théorie Nombres Bordeaux 21 (2009), 285–300.CrossRefGoogle Scholar
[248]Kedlaya, K.S., Swan conductors for p-adic differential modules, II: Global variation, J. Institut Math. Jussieu 10 (2011), 191–224.Google Scholar
[249]Kedlaya, K.S., Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuations, Compos. Math. 147 (2011), 467–523; errata in [255].Google Scholar
[250]Kedlaya, K.S., Good formal structures for flat meromorphic connections, I: Surfaces, Duke Math. J. 154 (2010), 343–418; erratum, ibid. 161 (2012), 733–734.Google Scholar
[251]Kedlaya, K.S., Good formal structures for flat meromorphic connections, II: Excellent schemes, J. Amer. Math. Soc. 24 (2011), 183–229.Google Scholar
[252]Kedlaya, K.S., Effective p-adic cohomology for cyclic cubic threefolds, in Computational Algebraic and Analytic Geometry, Contemp. Math. 572, Amer. Math. Soc., 2012, 127–171.Google Scholar
[253]Kedlaya, K.S., Nonarchimedean geometry of Witt vectors, Nagoya Math. J. 209 (2013), 111–165.Google Scholar
[254]Kedlaya, K.S., Reified valuations and adic spectra, Res. Number Theory 1 (2015), 1–42.Google Scholar
[255]Kedlaya, K.S., Local and global structure of connections on nonarchimedean curves, Compos. Math. 151 (2015), 1096–1156; errata in [269].Google Scholar
[256]Kedlaya, K.S., On commutative nonarchimedean Banach fields, Doc. Math. 23 (2018), 171–188.Google Scholar
[257]Kedlaya, K.S., Some ring-theoretic properties of Ainf, in p-adic Hodge Theory, Springer, 2020.Google Scholar
[258]Kedlaya, K.S., Sheaves, stacks, and shtukas, in [76], 58–205.Google Scholar
[259]Kedlaya, K.S., Convergence polygons for connections on nonarchimedean curves, in Nonarchimedean and Tropical Geometry, Simons Symposia, Springer Nature, 2016, 51–98.Google Scholar
[260]Kedlaya, K.S., Good formal structures on flat meromorphic connections, III: Irregularity and turning loci, arXiv:1308.5259v4 (2019); to appear in Publ. RIMS (Kashiwara 70th birthday issue).Google Scholar
[261]Kedlaya, K.S., Weil cohomology in practice, lecture notes (2019) available at http://kskedlaya.org/papers/.Google Scholar
[262]Kedlaya, K.S., Notes on isocrystals, arXiv:1606.01321v5 (2018).Google Scholar
[263]Kedlaya, K.S., Étale and crystalline companions, I, arXiv:1811.00204v3 (2020).Google Scholar
[264]Kedlaya, K.S., Étale and crystalline companions, II, arXiv:2008.13053v1 (2020).Google Scholar
[265]Kedlaya, K.S., Frobenius modules over multivariate Robba rings, arXiv:1311.7468v3 (2020).Google Scholar
[266]Kedlaya, K.S., Frobenius structures on hypergeometric equations, arXiv:1912.13073v2 (2021).Google Scholar
[267]Kedlaya, K.S., Litt, D., and Witaszek, J., Tamely ramified morphisms of curves and Belyi's theorem in positive characteristic, arXiv:2010.01130v1 (2020).Google Scholar
[268]Kedlaya, K.S. and Liu, R., Relative p-adic Hodge theory, II: Imperfect period rings, arXiv:1602.06899v3 (2019).Google Scholar
[269]Kedlaya, K.S. and Shiho, A., Corrigendum: Local and global structure of connections on nonarchimedean curves, Compos. Math. 153 (2017), 2658–2665.Google Scholar
[270]Kedlaya, K.S. and Tuitman, J., Effective bounds for Frobenius structures, Rend. Sem. Mat. Padova 128 (2012), 7–16.Google Scholar
[271]Kedlaya, K.S. and Xiao, Liang, Differential modules on p-adic polyannuli, J. Inst. Math. Jussieu 9 (2010), 155–201; erratum, ibid. 9 (2010), 669–671.Google Scholar
[272]Kiehl, R., Der Endlichkeitssatz für eigentliche Abbildungen in der nichtarchimedischen Funktiontheorie, Invent. Math. 2 (1967), 191–214.Google Scholar
[273]Kim, M., The non-abelian (or non-linear) method of Chabauty, in Noncommutative Geometry and Number Theory, Aspects Math. E37, Friedr. Vieweg, Wiesbaden, 2006, 179–185.Google Scholar
[274]Kisin, M., Overconvergent modular forms and the Fontaine-Mazur conjecture, Invent. Math. 153 (2003), 373–454.Google Scholar
[275]Kisin, M., Crystalline representations and F-crystals, in Algebraic Geometry and Number Theory, Progress in Math. 253, Birkhäuser, Boston, 2006, 459–496.Google Scholar
[276]Köpf, U., Über eigentliche familien algebraischer varietäten über affinoiden räumen, Schriftenreihe Math. Inst. Münster, 2. Serie. Heft 7 (1974).Google Scholar
[277]Kottwitz, R.E., Isocrystals with additional structure, Comp. Math. 56 (1985), 201–220.Google Scholar
[278]Kottwitz, R.E., Isocrystals with additional structure. II, Comp. Math. 109 (1997), 255–339.Google Scholar
[279]Kottwitz, R.E., On the Hodge-Newton decomposition for split groups, Int. Math. Res. Notices 26 (2003), 1433–1447.Google Scholar
[280]Krasner, M., Prolongement analytique uniform et multiforme dans le corps valués complets, Les Tendances Géom. en Algèbre et Théorie des Nombres, CNRS, Paris, 1966, 97–141.Google Scholar
[281]Krein, M., A principle of duality for bicompact groups and quadratic block algebras (Russian), Doklady Akad. Nauk. SSSR 69 (1949), 725–728.Google Scholar
[282]Kuhlmann, F.-V., Elimination of ramification I: The generalized stability theorem, Trans. Amer. Math. Soc. 362 (2010), no. 11, 5697–5727.Google Scholar
[283]Krull, W., Allgemeine Bewertungstheorie, J. für Math. 167 (1932), 160–196.Google Scholar
[284]Lafforgue, L., Chtoucas de Drinfeld et correspondance de Langlands, Invent. Math. 147 (2002), 1–241.Google Scholar
[285]Lang, S., Algebraic groups over finite fields, Amer. J. Math. 78 (1956), 555–563.Google Scholar
[286]Lauder, A.G.B., Deformation theory and the computation of zeta functions, Proc. London Math. Soc. 88 (2004), 565–602.Google Scholar
[287]Lauder, A.G.B. and Wan, D., Counting points on varieties over finite fields of small characteristic, in Algorithmic Number Theory, MSRI Pub. 44, Cambridge Univ. Press, Cambridge, 2008, 579–612.Google Scholar
[288]Laumon, G., Cohomology of Drinfeld Modular Varieties I, Cambridge Studies in Advanced Math. 41, Cambridge University Press, Cambridge, 1996.Google Scholar
[289]Lazard, M., Les zéros d’une fonction analytique d’une variable sur un corps valué complet, Publ. Math. IHÉS 14 (1962), 47–75.Google Scholar
[290]Levelt, A.H.M., Jordan decomposition for a class of singular differential operators, Ark. Mat. 13 (1975), 1–27.Google Scholar
[291]Le Stum, B., Rigid Cohomology, Cambridge Tracts in Math. 172, Cambridge University Press, Cambridge, 2007.Google Scholar
[292]Lindenstrauss, J. and Tzafriri, L., Classical Banach Spaces, Lecture Notes in Math. 338, Springer, 1973.Google Scholar
[293]Liu, R., Cohomology and duality for (φ, Γ)-modules over the Robba ring, Int. Math. Res. Notices 2007, article ID rnm150 (32 pages).Google Scholar
[294]Loday-Richaud, M., Stokes phenomenon, multisummability and differential Galois groups, Ann. Inst. Fourier (Grenoble) 44 (1994), 849–906.Google Scholar
[295]Loeser, F., Exposants p-adiques et théorèmes d’indice pour les équations différentielles p-adiques (d’après G. Christol et Z. Mebkhout), Séminaire Bourbaki, Vol. 1996/97, Astérisque 245 (1997), 57–81.Google Scholar
[296]Loewy, A., Über einen Fundamentalsatz für Matrizen oder lineare homogene Differentialsysteme, Sitzungsberichte der Heidelberger Akademie der Wissenschaften, 5. Abhandlung (1918), 1–36.Google Scholar
[297]Lubin, J., Nonarchimedean dynamical systems, Compositio Math. 94 (1994), 321–346.Google Scholar
[298]Lutz, E., Sur l’équation y2 = x3 + Ax + B sur les corps 𝔭-adiques, J. reine angew Math. 177 (1937), 238–247.Google Scholar
[299]Malgrange, B., Sur les points singuliers des équations différentielles, Enseign. Math. 20 (1974), 147–176.Google Scholar
[300]Malgrange, B., Équations Différentielles à coeffcients polynomiaux, Progress in Math. 96, Birkhäuser, Basel, 1991.Google Scholar
[301]Malgrange, B., Connexions méromorphes 2: Le réseau canonique, Invent. Math. 124 (1996), 367–387.Google Scholar
[302]Manin, Yu. I., The theory of commutative formal groups over fields of finite characteristic (Russian), Usp. Math. 18 (1963), 3–90; English translation, Russian Math. Surveys 18 (1963), 1–80.Google Scholar
[303]Manjra, S., A note on non-Robba p-adic differential equations, Proc. Japan Acad. Ser. A 87 (2011), 40–43.Google Scholar
[304]Marmora, A., Irrégularité et conducteur de Swan p-adiques, Doc. Math. 9 (2004), 413–433.Google Scholar
[305]Matignon, M. and Reversat, M., Sous-corps fermés d’un corps valué, J. Algebra 90 (1984), 491–515.Google Scholar
[306]Matsuda, S., Local indices of p-adic differential operators corresponding to Artin-Schreier-Witt coverings, Duke Math. J. 77 (1995), 607–625.Google Scholar
[307]Matsuda, S., Katz correspondence for quasi-unipotent overconvergent isocrystals, Comp. Math. 134 (2002), 1–34.Google Scholar
[308]Matsuda, S., Conjecture on Abbes-Saito filtration and Christol-Mebkhout filtration, in Geometric Aspects of Dwork Theory. Vol. I, II, de Gruyter, Berlin, 2004, 845–856.Google Scholar
[309]Mebkhout, Z., Analogue p-adique du théorème de Turrittin et le théorème de la monodromie p-adique, Invent. Math. 148 (2002), 319–351.Google Scholar
[310]Mochizuki, T., Good formal structure for meromorphic flat connections on smooth projective surfaces, in Miwa, T. et al. (eds.), Algebraic Analysis and Around, Advanced Studies in Pure Math. 54, Math. Soc. Japan, 2009, 223–253.Google Scholar
[311]Mochizuki, T., Wild harmonic bundles and wild pure twistor D-modules, Astérisque 340 (2011).Google Scholar
[312]Mochizuki, T., The Stokes structure of a good meromorphic flat bundle, J. Inst. Math. Jussieu 10 (2011), 675–712.Google Scholar
[313]Monsky, P., Formal cohomology, II: The cohomology sequence of a pair, Ann. of Math. 88 (1968), 218–238.Google Scholar
[314]Monsky, P., Formal cohomology, III: Fixed point theorems, Ann. of Math. 93 (1971), 315–343.Google Scholar
[315]Monsky, P. and Washnitzer, G., Formal cohomology, I, Ann. of Math. 88 (1968), 181–217.Google Scholar
[316]Morita, K., Crystalline and semi-stable representations in the imperfect residue field case, Asian J. Math. 18 (2014), 143–157.Google Scholar
[317]Mumford, D., Fogarty, J., Kirwan, F., Geometric Invariant Theory, third edition, Ergebnisse der Math. 34, Springer-Verlag, Berlin, 1994.Google Scholar
[318]Munkres, J.R., Topology, second edition, Prentice Hall, Saddle River, 2000.Google Scholar
[319]Nagata, M., Local Rings, Interscience Tracts in Pure and Applied Math. 13, John Wiley & Sons, New York, 1962.Google Scholar
[320]Nicaise, J., Berkovich skeleta and birational geometry, in Nonarchimedean and Tropical Geometry, Simons Symposia, Springer, Cham, 2016, 173–194.Google Scholar
[321]Ohkubo, S., The p-adic monodromy theorem in the imperfect residue field case, Algebra Number Theory 7 (2013), 1977–2037.Google Scholar
[322]Ohkubo, S., A note on logarithmic growth Newton polygons of p-adic differential equations, Int. Math. Res. Notices 2014, paper ID rnu017.Google Scholar
[323]Ohkubo, S., On differential modules associated to de Rham representations in the imperfect residue field case, Algebra Number Theory 9 (2015), 1881–1954.Google Scholar
[324]Ohkubo, S., On the rationality and continuity of logarithmic growth filtration of solutions of p-adic differential equations, Adv. Math. 308 (2017), 83–120.Google Scholar
[325]Ohkubo, S., A note on logarithmic growth of solutions of p-adic differential equations without solvability, Math. Res. Lett. 26 (2019), 1527–1557.Google Scholar
[326]Ohkubo, S., Logarithmic growth filtrations for (φ, ∇)-modules over the bounded Robba ring, Compos. Math. 157 (2021), 1265–1301.Google Scholar
[327]Ohtsuki, M., A residue formula for Chern classes associated with logarithmic connections, Tokyo J. Math. 5 (1982), 13–21.Google Scholar
[328]Oort, F. and Zink, T., Families of p-divisible groups with constant Newton polygon, Doc. Math. 7 (2002), 183–201.Google Scholar
[329]Ore, O., Theory of non-commutative polynomials, Annals of Math. 34 (1933), 480–508.Google Scholar
[330]Osserman, B., The Weil conjectures, in The Princeton Companion to Mathematics, Princeton University Press, Princeton, 2008.Google Scholar
[331]Ostrowski, A., Untersuchungen zur arithmetischen Theorie der Körper, Math. Z. 39 (1935), 269–404.Google Scholar
[332]Pancratz, S. and Tuitman, J., Improvements to the deformation method for counting points on smooth projective hypersurfaces, Found. Comput. Math. 15 (2015), 1413–1464.Google Scholar
[333]Payne, S., Analytification is the limit of all tropicalizations, Math. Res. Lett. 16 (2009), 543–556.Google Scholar
[334]Pila, J., Frobenius maps of abelian varieties and finding roots of unity in finite fields, Math. Comp. 55 (1990), 745–763.Google Scholar
[335]Poineau, J. and Pulita, A., The convergence Newton polygon of a p-adic differential equation II: Continuity and finiteness on Berkovich curves, Acta Math. 214 (2015), 357–393.Google Scholar
[336]Poineau, J. and Pulita, A., Continuity and finiteness of the radius of convergence of a p-adic differential equation via potential theory, J. reine angew. Math. 707 (2015), 125–147.Google Scholar
[337]Poineau, J. and Pulita, A., The convergence Newton polygon of a p-adic differential equation III: global decomposition and controlling graphs, arXiv:1308.0859v1 (2013).Google Scholar
[338]Poineau, J. and Pulita, A., The convergence Newton polygon of a p-adic differential equation IV: local and global index theorems, arXiv:1309.3940v2 (2014).Google Scholar
[339]Pons, E., Modules différentiels non solubles. Rayons de convergence et indices, Rend. Sem. Mat. Univ. Padova 103 (2000), 21–45.Google Scholar
[340]Poonen, B., Maximally complete fields, Enseign. Math. (2) 39 (1993), 87–106.Google Scholar
[341]Priess-Crampe, S. and Ribenboim, P., Differential equations over valued fields (and more), J. reine angew. Math. 576 (2004), 123–147.Google Scholar
[342]Pulita, A., Frobenius structure for rank one p-adic differential equations, in Ultrametric functional analysis, Contemp. Math. 384, Amer. Math. Soc., Providence, 2005, 247–258.Google Scholar
[343]Pulita, A., Rank one solvable p-adic differential equations and finite Abelian characters via Lubin-Tate groups, Math. Ann. 337 (2007), 489–555.Google Scholar
[344]Pulita, A., Small connections are cyclic, arXiv:1407.3761v1 (2014).Google Scholar
[345]Pulita, A., The convergence Newton polygon of a p-adic differential equation I: Affinoid domains of the Berkovich affine line, Acta Math. 214 (2015), 307–355.Google Scholar
[346]Ramis, J.-P., Théorèmes d’indices Gevrey pour les équations différentielles ordinaires, Mem. Amer. Math. Soc. 48 (1984).Google Scholar
[347]Ribenboim, P., The Theory of Classical Valuations, Springer-Verlag, New York, 1999.Google Scholar
[348]Ritt, J.F., Differential Algebra, Colloq. Pub. XXXIII, Amer. Math. Soc., New York, 1950.Google Scholar
[349]Robba, P., On the index of p-adic differential operators. I, Ann. Math. 101 (1975), 280–316.Google Scholar
[350]Robba, P., Lemmes de Hensel pour les opérateurs différentiels. Application à la réduction formelle des équations différentielles, Enseign. Math. (2) 26 (1980), 279–311.Google Scholar
[351]Robba, P., On the index of p-adic differential operators. II, Duke Math. J. 43 (1976), 19–31.Google Scholar
[352]Robba, P., Index of p-adic differential operators. III. Application to twisted exponential sums, Astérisque 119–120 (1984), 191–266.Google Scholar
[353]Robba, P., Indice d’un opérateur différentiel p-adique. IV. Cas des systèmes. Mesure de l’irrégularité dans un disque. Ann. Inst. Fourier (Grenoble), 35 (1985), 13–55.Google Scholar
[354]Robba, P., Une introduction naïve aux cohomologies de Dwork, Mém. Soc. Math. France 23 (1986), 61–105.Google Scholar
[355]Robert, A.M., A Course in p-adic Analysis, Graduate Texts in Math. 198, Springer-Verlag, New York, 2000.Google Scholar
[356]Robertson, E. and O’Connor, J. (eds.), MacTutor History of Mathematics Archive, https://mathshistory.st-andrews.ac.uk (retrieved July 2020).Google Scholar
[357]Rockafellar, R.T., Convex Analysis, Princeton University Press, Princeton, 1970.Google Scholar
[358]Rivano, N. Saavedra, Catégories Tannakiennes, Lecture Notes in Math. 265. Springer-Verlag, Berlin, 1972.Google Scholar
[359]Sabbah, C., Introduction to Stokes Structures, Lecture Notes in Math. 2060, Springer, Heidelberg, 2013.Google Scholar
[360]Savitt, D. and Thakur, D. (eds.), p-adic Geometry: Lectures from the 2007 Arizona Winter School, Univ. Lecture Series 45, Amer. Math. Soc., 2008.Google Scholar
[361]Schikhof, W.H., Ultrametric Calculus: An Introduction to p-adic Analysis, Cambridge Studies in Advanced Math. 4, Cambridge University Press, Cambridge, 1984.Google Scholar
[362]Schmid, W., Variation of Hodge structure: the singularities of the period mapping, Invent. Math. 22 (1973), 211–319.Google Scholar
[363]Schneider, P., Nonarchimedean Functional Analysis, Springer-Verlag, Berlin, 2002.Google Scholar
[364]Schoof, R., Elliptic curves over finite fields and the computation of square roots mod p, Math. Comp. 44 (1985), 483–494.Google Scholar
[365]Scholze, P., Perfectoid spaces, Publ. Math. IHÉS 116 (2012), 245–313.Google Scholar
[366]Scholze, P. and Weinstein, J., Berkeley Lectures on p-adic Geometry, Annals of Math. Studies 207, Princeton University Press, Princeton, 2020.Google Scholar
[367]Schörner, E., Ultrametric fixed point theorems and applications, in Valuation Theory and its Applications, Vol. II (Saskatoon, SK, 1999), Fields Inst. Communications 33, Amer. Math. Soc., 2003, 353–359.Google Scholar
[368]Serre, J.-P., Géométrie algébrique et géométrie analytique, Ann. Inst. Fourier. 6 (1956), 1–42.Google Scholar
[369]Serre, J.-P., Local Fields, Graduate Texts in Math. 67, Springer-Verlag, New York, 1979.Google Scholar
[370]Serre, J.-P., Galois cohomology, Corrected reprint of the 1997 English edition, Springer Monographs in Math., Springer-Verlag, Berlin, 2002.Google Scholar
[371]Sertöz, E.C., Computing periods of hypersurfaces, Math. Comp. 88 (2019), 2987–3022.Google Scholar
[372]Sibuya, Y., Stokes phenomena, Bull. Amer. Math. Soc. 83 (1977), 1075–1077.Google Scholar
[373]Silverman, J.H., The Arithmetic of Elliptic Curves, second printing, Graduate Texts in Math. 106, Springer-Verlag, New York, 1991.Google Scholar
[374]Singer, M.F. and van der Put, M., Galois Theory of Difference Equations, Lecture Notes in Math. 1666, Springer-Verlag, Berlin, 1997.Google Scholar
[375]Singer, M.F. and van der Put, M., Galois Theory of Linear Differential Equations, Grundlehren der Math. Wiss. 328, Springer-Verlag, Berlin, 2003.Google Scholar
[376]Sperber, S. and Voight, J., Computing zeta functions of nondegenerate hypersurfaces with few monomials, LMS J. Comput. Math. 16 (2013), 9–44.Google Scholar
[377]Springer, T.A., Linear Algebraic Groups, second edition, Birkäuser, Boston, 1991.Google Scholar
[378]The Stacks Project Authors, Stacks Project, http://stacks.math.columbia.edu (retrieved Feb 2020).Google Scholar
[379]Stokes, G.G., On the discontinuity of arbitrary constants which appear in divergent developments, Trans. Cambridge Phil. Soc. 10 (1857), 106–128.Google Scholar
[380]Sugiyama, Y. and Yasuda, S., Belyi's theorem in characteristic two, Compos. Math. 156 (2020), 325–339.Google Scholar
[381]Tannaka, T., Über den Dualitätsatz der nichtkommutativen topologischen Gruppen, Tôhoku Math. J. 45 (1938), 1–12.Google Scholar
[382]Tate, J., p-divisible groups, in Proceedings of a Conference on Local Fields (Driebergen, 1966), Springer-Verlag, Berlin, 1967, 158–183.Google Scholar
[383]Temkin, M., Stable modification of relative curves, J. Alg. Geom. 19 (2010), 603–677.Google Scholar
[384]Temkin, M., Metric uniformization of morphisms of Berkovich curves, Adv. Math. 317 (2017), 438–472.Google Scholar
[385]Terasoma, T., Confluent hypergeometric functions and wild ramification, J. Algebra 185 (1996), 1–18.Google Scholar
[386]Teyssier, J.-B., Skeletons and moduli of Stokes torsors, Ann. Sci. Éc. Norm. Sup. 52 (2019), 337–365.Google Scholar
[387]Teyssier, J.-B., Higher dimensional Stokes structures are rare, in A Panorama of Singularities, Contemp. Math. 742, Amer. Math. Soc., Providence, RI, 2020, 201–217.Google Scholar
[388]Teyssier, J.-B., Moduli of Stokes torsors and singularities of differential equations, to appear in J. Eur. Math. Soc. (2021).Google Scholar
[389]Thuillier, A., Théorie du potentiel sur les courbes en géométrie analytique non archimédienne. Applications à la theorie d’Arakelov, thesis, Université de Rennes 1, 2005.Google Scholar
[390]Thuillier, A., Géométrie toroïdale et géométrie analytique non archimédienne. Application au type d’homotopie de certains schémas formels, Manuscripta Math. 123 (2007), 381–451.Google Scholar
[391]Turrittin, H.L., Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point, Acta Math. 93 (1955), 27–66.Google Scholar
[392]Tsuzuki, N. (as Nobuo, T.), The overconvergence of morphisms of étale φ-∇-spaces on a local field, Compos. Math. 103 (1996), 227–239.Google Scholar
[393]Tsuzuki, N., Finite local monodromy of overconvergent unit-root F-isocrystals on a curve, Amer. J. Math. 120 (1998), 1165–1190.Google Scholar
[394]Tsuzuki, N., The local index and the Swan conductor, Comp. Math. 111 (1998), 245–288.Google Scholar
[395]Tsuzuki, N., Slope filtration of quasi-unipotent overconvergent F-isocrystals, Ann. Inst. Fourier (Grenoble) 48 (1998), 379–412.Google Scholar
[396]Tsuzuki, N., Morphisms of F-isocrystals and the finite monodromy theorem for unit-root F-isocrystals, Duke Math. J. 111 (2002), 385–419.Google Scholar
[397]Tsuzuki, N., On base change theorem and coherence in rigid cohomology, Kazuya Kato's fiftieth birthday, Doc. Math. 2003 Extra Vol., 891–918.Google Scholar
[398]Tsuzuki, N., Minimal slope conjecture of F-isocrystals, arXiv:1910.03871v2 (2019).Google Scholar
[399]Tuitman, J., Counting points on curves using a map to P1, Math. Comp. 85 (2016), 961–981.Google Scholar
[400]Tuitman, J., Counting points on curves using a map to P1, II, Finite Fields Appl. 45 (2017), 301–322.Google Scholar
[401]Tuitman, J., Computing zeta functions of generic projective hypersurfaces in larger characteristic, Math. Comp. 88 (2019), 439–451.Google Scholar
[402]van der Put, M., The cohomology of Monsky and Washnitzer, Introductions aux cohomologies p-adiques (Luminy, 1984), Mém. Soc. Math. France 23 (1986), 33–59.Google Scholar
[403]van Rooij, A.C.M., Non-Archimedean Functional Analysis, Monographs and Textbooks in Pure and Applied Math. 51, Marcel Dekker, New York, 1978.Google Scholar
[404]Vaquié, M., Valuations, in Resolution of singularities (Obergurgl, 1997), Progr. Math. 181, Birkhäuser, Basel, 2000, 539–590.Google Scholar
[405]Varadarajan, V.S., Linear meromorphic differential equations: a modern point of view, Bull. Amer. Math. Soc. 33 (1996), 1–42.Google Scholar
[406]Wasow, W., Asymptotic Expansions for Ordinary Differential Equations, reprint of the 1976 edition, Dover, New York, 1987.Google Scholar
[407]Weibel, C.A., An Introduction to Homological Algebra, Cambridge Studies in Advanced Math. 38, Cambridge University Press, Cambridge, 1994.Google Scholar
[408]Weyl, H., Das asymptotische Verteilungsgesetz der Eigenwerte linearer partieller Differentialgleichungen (mit einer Anwendung auf die Theorie der Hohlraumstrahlung), Math. Ann. 71 (1912), 441–479.Google Scholar
[409]Weyl, H., Inequalities between the two kinds of eigenvalues of a linear transformation, Proc. Nat. Acad. Sci. USA 35 (1949), 408–411.Google Scholar
[410]Xiao, L., Non-archimedean differential modules and ramification theory, thesis, Massachusetts Institute of Technology, 2009.Google Scholar
[411]Xiao, L., On ramification filtrations and p-adic differential equations, I: the equal characteristic case, Algebra Number Theory 4 (2010), 969–1027.Google Scholar
[412]Xiao, L., On ramification filtrations and p-adic differential equations, II: mixed characteristic case, Compos. Math. 148 (2012), 415–463.Google Scholar
[413]Xiao, L., On the refined ramification filtrations in the equal characteristic case, Alg. Number Theory 6 (2012), 1579–1667.Google Scholar
[414]Ye, S., A group-theoretic generalization of the p-adic local monodromy theorem, arXiv:2004.01224v2 (2020).Google Scholar
[415]Young, P.T., Radii of convergence and index for p-adic differential operators, Trans. Amer. Math. Soc. 333 (1992), 769–785.Google Scholar
[416]Zassenhaus, H., Über eine Verallgemeinerung des Henselschen Lemmas, Arch. Math. (Basel) 5 (1954), 317–325.Google Scholar
[417]Zhukov, I.B., A approach to higher ramification theory, in Invitation to higher local fields (Münster, 1999), Geom. Topol. Monographs 3, Geom. Topol. Publ., Coventry, 2000, 143–150.Google Scholar
[418]Zhukov, I.B., On ramification theory in the case of an imperfect residue field (Russian), Mat. Sb. 194 (2003), 3–30; translation, Sb. Math. 194 (2003), 1747–1774.Google Scholar
[419]Zink, T., On the slope filtration, Duke Math. J. 109 (2001), 79–95.Google Scholar

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  • References
  • Kiran S. Kedlaya, University of California, San Diego
  • Book: p-adic Differential Equations
  • Online publication: 06 August 2022
  • Chapter DOI: https://doi.org/10.1017/9781009127684.041
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