On {$l$}-adic iterated integrals. I. Analog of Zagier conjecture

On {$l$}-adic iterated integrals. I. Analog of Zagier conjecture

Zdzisław Wojtkowiak

Source: Nagoya Math. J. Volume 176 (2004), 113-158.

Abstract

We are studying some aspects of the action of Galois groups on the torsor of paths connecting two (possibly tangential) points on a projective 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.

First Page: Show

Related Works:

See also: "On {$l$}-adic iterated integrals. II. Functional equations and $l$-adic iterated polylogarithms," by Zdzisław Wojtkowiak. Nagoya Math. J., vol. 177 (2005), pp. 117--153.

Project Euclid: euclid.nmj/1114632160

See also: "On {$l$}-adic iterated integrals. III. Galois actions on fundamental groups," by Zdzisław Wojtkowiak. Nagoya Math. J., vol. 178 (2005), pp. 1--36.

Project Euclid: euclid.nmj/1124217069

Primary Subjects: 11G55

Secondary Subjects: 14G32

Full-text: Open access

PDF File (304 KB)

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.nmj/1114632124
Mathematical Reviews number (MathSciNet): MR2108125
Zentralblatt MATH identifier: 02211521

back to Table of Contents

References

G. W. Anderson and Y. Ihara, Pro-$l$ branched coverings of $\BP^{1}$ and higher circular $l$-units. Part $2$ , International Journal of Mathematics, Volume 1, No 2 (1990), 119–148.

Mathematical Reviews (MathSciNet): MR1060632

Zentralblatt MATH: 0715.14021

Digital Object Identifier: doi:10.1142/S0129167X90000095

A. A. Beilinson and P. Deligne, Interprétation motivique de la conjecture de Zagier reliant polylogarithmes et régulareurs (U. Jannsen, S. L. Kleiman and J.-P. Serre, Motives, eds.), Proc. of Symp. in Pure Math. 55, Part II, AMS (1994), 97–121.

Mathematical Reviews (MathSciNet): MR1265552

P. Deligne, 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), 79–297.

Mathematical Reviews (MathSciNet): MR1012168

Zentralblatt MATH: 0742.14022

W. G. Drinfeld, On quasitriangular quasi-Hopf algebras and a group closely connected with $\Gal(\bar \Q/\Q)$ , Algebra i Analiz, 2 (1990), 114–148 ; English translation, Leningrad Math. J., 2 (4) (1991), 829–860.

Mathematical Reviews (MathSciNet): MR1047964

Y. Ihara, Profinite braid groups, Galois representations and complex multiplications , Annals of Math., 123 (1986), 43–106.

Mathematical Reviews (MathSciNet): MR825839

Digital Object Identifier: doi:10.2307/1971352

JSTOR: links.jstor.org

Y. Ihara, Braids, Galois Groups and Some Arithmetic Functions, , Proc. of the Int. Cong. of Math. Kyoto (1990), 99–119.

Mathematical Reviews (MathSciNet): MR1128323

Zentralblatt MATH: 0757.20007

W. Magnus, A. Karrass, D. Solitar, Combinatorial Group Theory, Pure and Applied Mathematics, XIII, Interscience Publishers (1966).

H. Nakamura, Galois rigidity of pure sphere braid groups and profinite calculus , J. Math. Sci. Univ. Tokyo, 1 (1994), 71–136.

Mathematical Reviews (MathSciNet): MR1298541

H. Nakamura, Tangential base points and Eisenstein series , Aspects of Galois Theory (H. Volklein, D. Harbater, P. Muller and J. Thompson, eds.), London Math. Society Lecture Note Series 256 (1999), 202–217.

Mathematical Reviews (MathSciNet): MR1708607

Zentralblatt MATH: 0986.14013

H. Nakamura and H. Tsunogai, Some finiteness theorems on Galois centralizers in pro-$l$ mapping class groups , Journal fur die reine und angewandte Mathematik, 441 (1993), 115–144.

Mathematical Reviews (MathSciNet): MR1228614

Ch. Soulé, K-théorie des anneaux d`entiers de corps de nombres et cohomologie étale , Inventiones math., 55 , 251–295 (1979).

Mathematical Reviews (MathSciNet): MR553999

Digital Object Identifier: doi:10.1007/BF01406843

Ch. Soulé, On higher $p$-adic regulators , Springer Lecture Notes N 854 (1981), 372–401.

Mathematical Reviews (MathSciNet): MR618313

Ch. Soulé, Eléments Cyclotomiques en K-Théorie , Asterisque, 147–148 (1987), 225–258.

Mathematical Reviews (MathSciNet): MR891430

Z. Wojtkowiak, The Basic Structure of Polylogarithmic Functional Equations , Structural Properties of Polylogarithms (L. Lewin, ed.), Mathematical Surveys and Monographs, Vol 37, 205–231.

Mathematical Reviews (MathSciNet): MR1148381

Z. Wojtkowiak, Monodromy of iterated integrals and non-abelian unipotent periods , Geometric Galois Actions London Math. Soc. L.N. Series 243, Cambridge University Press, 219–289.

Mathematical Reviews (MathSciNet): MR1653015

Digital Object Identifier: doi:10.1017/CBO9780511666124.011

Z. Wojtkowiak, Mixed Hodge Structures and Iterated Integrals I , Motives, Polylogarithms and Hodge Theory. Part I: Motives and Polylogarithms, International Press Lecture Series Vol. 3, Part I (2002), 121–208.

Mathematical Reviews (MathSciNet): MR1977586

Zentralblatt MATH: 1051.14011

Z. Wojtkowiak, On $l$-adic iterated integrals , Prépublication n 603, Université de Nice (2000).

previous :: next

Nagoya Mathematical Journal

Credits

Turn MathJax Off
What is MathJax?