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Around the Grothendieck anabelian section conjecture

Published online by Cambridge University Press:  05 January 2012

By
Mohamed Saïdi
Edited by
John Coates ,
Minhyong Kim ,
Florian Pop ,
Mohamed Saïdi  and
Peter Schneider
Mohamed Saïdi
Affiliation:
University of Exeter
John Coates
Affiliation:
University of Cambridge
Minhyong Kim
Affiliation:
University College London
Florian Pop
Affiliation:
University of Pennsylvania
Mohamed Saïdi
Affiliation:
University of Exeter
Peter Schneider
Affiliation:
Universität Münster
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Chapter
Information
Non-abelian Fundamental Groups and Iwasawa Theory , pp. 72 - 106
Publisher: Cambridge University Press
Print publication year: 2011

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References

[1] Esnault, H., Wittenberg, O., Remarks on cycle classes of sections of the fundamental group. Mosc. Math. J. 9 (2009), no. 3, 451–467.Google Scholar
[2] Esnault, H., Wittenberg, O., On abelian birational sections. Journal of the American Mathematical Society, 23 (2010), no. 3, 713–724.CrossRefGoogle Scholar
[3] Grothendieck, A., Revêtements étales et groupe fondamental. Séminaire de géométrie algébrique du Bois Marie1960–61.
[4] Grothendieck, A., Brief an G., Faltings (German with an English translation on pp. 285–293). London Math. Soc. Lecture Note Ser., 242, Geometric Galois actions, 1, 49-58, Cambridge University Press, Cambridge, 1997.Google Scholar
[5] Hoshi, Y., Existence of nongeometric pro-p Galois sections of hyperbolic curves. To appear in Publications of RIMS.
[6] Koenigsmann, J., On the section conjecture in anabelian geometry. J. Reine Angew. Math. 588 (2005), 221–235.CrossRefGoogle Scholar
[7] Mochizuki, S., Absolute anabelian cuspidalizations of proper hyperbolic curves. J. Math. Kyoto Univ. 47 (2007), no. 3, 451–539.CrossRefGoogle Scholar
[8] Mochizuki, S., The local pro-p anabelian geometry of curves. Invent. Math. 138 (1999), no. 2, 319–423.CrossRefGoogle Scholar
[9] Mochizuki, S., Topics surrounding the anabelian geometry of hyperbolic curves. Galois groups and fundamental groups, 119–165, Math. Sci. Res. Inst. Publ., 41, Cambridge University Press, Cambridge, 2003.Google Scholar
[10] Mochizuki, S., Galois sections in absolute anabelian geometry. Nagoya Math. J. 179 (2005), 17–45.CrossRefGoogle Scholar
[11] Mochizuki, S., The absolute anabelian geometry of hyperbolic curves. Galois theory and modular forms, 77–122, Dev. Math., 11, Kluwer, Boston, 2004.Google Scholar
[12] Mochizuki, S., Topics in absolute anabelian geometry II: decomposition groups and endomorphisms. Preprint. Available in the home web page of Shinichi Mochizuki.
[13] Pop., F., On the birational p-adic section Conjecture, Compositio Math. 146 (2010), no. 3, 621–637.CrossRefGoogle Scholar
[14] Saïdi, M., Good sections of arithmetic fundamental groups. Manuscript.
[15] Saïdi, M., Tamagawa, A., A prime-to-p version of the Grothendieck anabelian conjecture for hyperbolic curves over finite fields of characteristic p > 0. Publ. Res. Inst. Math. Sci. 45 (2009), no. 1, 135–186.CrossRefGoogle Scholar
[16] Tamagawa, A., The Grothendieck conjecture for affine curves. Compositio Math. 109 (1997), no. 2, 135–194.CrossRefGoogle Scholar

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