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On i-Adic Iterated integrals, I analog of zagier conjecture

Published online by Cambridge University Press:  22 January 2016

ZdzisLaw Wojtkowiak
ZdzisLaw Wojtkowiak*
Affiliation:
Université de Nice-Sophia Antipolis, Département de Mathématiques, Laboratoire Jean Alexandre Dieudonné, U.R.A. au C.N.R.S., No 168, Parc Valrose- B.P.N° 71, 06108 NiceCedex 2, France. wojtkow@math.unice.fr
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Abstract

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We are studying some aspects of the action of Galois groups on the torsor of paths connecting two (possibly tangential) points on a projec-tive line minus a finite number of points. We obtain objects which formally behave like classical iterated integrals and polylogarithms. We formulate an analog of Zagier conjecture for these l-adic analogs of iterated integrals and polylogarithms.

Keywords

11G5511G9914G32
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 176 , 2004 , pp. 113 - 158
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

References

[AI] Anderson, G. W. and Ihara, Y., Pro-l branched coverings of P1 and higher circular l-units. Part 2, International Journal of Mathematics, Volume 1, No 2 (1990), 119–148.Google Scholar
[BD] Beilinson, A. A. and Deligne, P., Interprétation motivique de la conjecture de Za-gier reliant polylogarithmes et régulareurs, Motives (Jannsen, U., Kleiman, S. L. and Serre, J.-P., eds.), Proc. of Symp. in Pure Math. 55, Part II, AMS (1994), pp. 97–121.Google Scholar
[D] Deligne, P., Le groupe fondamental de la droite projective moins trois points, Galois Groups over Q (Ihara, Y., Ribet, K. and Serre, J.-P., eds.), Mathematical Sciences Research Institute Publications, no 16 (1989), pp. 79–297.Google Scholar
[Dr] Drinfeld, W. G., On quasitriangular quasi-Hopf algebras and a group closely connected with Gal(Q/Q), Algebra i Analiz, 2 (1990), 114–148; English translation, Leningrad Math. J., 2 (4) (1991), 829–860.Google Scholar
[I1] Ihara, Y., Profinite braid groups, Galois representations and complex multiplications, Annals of Math., 123 (1986), 43–106.Google Scholar
[I2] Ihara, Y., Braids, Galois Groups and Some Arithmetic Functions, Proc. of the Int. Cong. of Math. Kyoto (1990), 99–119.Google Scholar
[MKS] Magnus, W., Karrass, A., Solitar, D., Combinatorial Group Theory, Pure and Applied Mathematics, XIII, Interscience Publishers, 1966.Google Scholar
[N1] Nakamura, H., Galois rigidity of pure sphere braid groups and profinite calculus, J. Math. Sci. Univ. Tokyo, 1 (1994), 71–136.Google Scholar
[N2] Nakamura, H., Tangential base points and Eisenstein series, Aspects of Galois Theory (Volklein, H., Harbater, D., Muller, P. and Thompson, J., eds.), London Math. Society Lecture Note Series 256 (1999), pp. 202–217.Google Scholar
[NT] Nakamura, H. and Tsunogai, H., Some finiteness theorems on Galois centralizers in pro-l mapping class groups, Journal fur die reine und angewandte Mathematik, 441 (1993), 115–144.Google Scholar
[S1] Soulé, Ch., K-théorie des anneaux d’entiers de corps de nombres et cohomologie étale, Inventiones math., 55 (1979), 251–295.CrossRefGoogle Scholar
[S2] Soulé, Ch., On higher p-adic regulators, Springer Lecture Notes N 854 (1981), 372–401.Google Scholar
[S3] Soulé, Ch., Eléments Cyclotomiques en K-Théorie, Asterisque, 147–148 (1987), 225–258.Google Scholar
[W1] Wojtkowiak, Z., The Basic Structure of Polylogarithmic Functional Equations, Structural Properties of Polylogarithms (Lewin, L., ed.), Mathematical Surveys and Monographs, Vol 37, pp. 205–231.CrossRefGoogle Scholar
[W2] Wojtkowiak, Z., Monodromy of iterated integrals and non-abelian unipotent periods, Geometric Galois Actions London Math. Soc. L.N. Series 243, Cambridge University Press, pp. 219–289.Google Scholar
[W3] Wojtkowiak, Z., Mixed Hodge Structures and Iterated Integrals I, Motives, Poly-logarithms and Hodge Theory. Part I: Motives and Polylogarithms, International Press Lecture Series Vol. 3, Part I (2002), pp. 121–208.Google Scholar
[W4] Wojtkowiak, Z., On l-adic iterated integrals, Prépublication n 603, Université de Nice (2000).Google Scholar