Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T23:53:53.515Z Has data issue: false hasContentIssue false
  • English
  • Français

On l-Adic Iterated Integrals, III Galois Actions on Fundamental Groups

Published online by Cambridge University Press:  11 January 2016

Zdzisław Wojtkowiak
Zdzisław 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 Nice Cedex 2, France, wojtkow@math.unice.fr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We continue to study l-adic iterated integrals introduced in the first part. We shall calculate explicitly l-adic logarithm and l-adic polylogarithms. Next we shall use these results to study Galois representations on the fundamental group of .

Keywords

11G5511G9914G32
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 178 , 2005 , pp. 1 - 36
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2005

References

[D1] Deligne, P., Le groupe fondamental de la droite projective moins trois points, Galois Groups over Q (Y. Ihara, K. Ribet and J.-P. Serre, eds.), Mathematical Sciences Research Institute Publications, no 16 (1989), pp. 79–297.Google Scholar
[D2] Deligne, P., talk on the conference in Schloss Ringberg (1998).Google Scholar
[G] Goncharov, A., The dihedral Lie algebra and Galois symmetries of π1 (1)(P1\({0, ∞} ∪ μN)), Duke Math. J., 110 (2001), 397–486.Google Scholar
[HW] Huber, A. and Wildeshaus, J., Classical motivic polylogarithm according to Beilinson and Deligne, Documenta Mathematica, 3 (1998), 27–113.Google Scholar
[I1] Ihara, Y., Profinite braid groups, Galois representations and complex multiplications, Annals of Math., 123 (1986), 43–106.CrossRefGoogle Scholar
[I2] Ihara, Y., Braids, Galois Groups and Some Arithmetic Functions, Proc. of the Int. Cong. of Math. Kyoto (1990), 99–119.Google Scholar
[IS] Ichimura, H. and Sakaguchi, K., The Non-Vanishing of a Certain Kummer Character χm (after Soulé) and Some Related Topics, Advanced Studies in Pure Mathematics 12 (1987), pp. 53–64.CrossRefGoogle Scholar
[NW] Nakamura, H. and Wojtkowiak, Z., On explicit formulae for l-adic polylogarithms, Arithmetic Fundamental Groups and Noncommutative Algebra (M. Fried and Y. Ihara, eds.), Proceedings of Symposia in Pure Mathematics, Vol. 70, American Mathematical Society, pp. 285–294.Google Scholar
[S1] Soulè, Ch., K-thèorie des anneaux d’entiers de corps de nombres et cohomologie etale, Inventiones math., 55 (1979), 251–295.CrossRefGoogle Scholar
[S2] Soulè, Ch., On higher p-adic regulators, Springer Lecture Notes N 854 (1981), 372–401.Google Scholar
[S3] Soulè, Ch., Elèments Cyclotomiques en K-Thèorie, Asterisque, 147–148 (1987), 225–258.Google Scholar
[Wa] Washington, L. C., Introduction to Cyclotomic Fields, Springer-Verlag, 1997.CrossRefGoogle Scholar
[W1] Wojtkowiak, Z., Monodromy of iterated integrals and Galois action on the fundamental group of a projective line minus a finite number of points, Prèpublication n 578, Universitè de Nice, 2000.Google Scholar
[W2] Wojtkowiak, Z., A note on functional equations of l-adic polylogarithms, Journal of the Inst. of Math. Jussieu, 3 (2004), no. 3, 461–471.CrossRefGoogle Scholar
[W3] Wojtkowiak, Z., Non-Abelian Unipotent Periods and Monodromy of Iterated Integrals, Journal of the Inst. of Math. Jussieu, 2 (2003), no. 1, 1–24.Google Scholar