Skip to main content Accessibility help
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 1
  • Print publication year: 2011
  • Online publication date: January 2012

Tensor and homotopy criteria for functional equations of ℓ-adic and classical iterated integrals

[BD] A., Beilinso, P., Deligne, Interprétation motivique de la conjecture de Zagier reliant polylogarithms et régulateurs, Proc. Symp. in Pure Math. (AMS) 55-2 (1994), 97–121.
[Bl1] S., Bloch, Applications of the dilogarithm function in algebraic K-theory and algebraic geometry, Proc. Int. Symp. Alg. Geom., Kyoto, (1977), 1–14.
[Bl2] S., Bloch, Function Theory of Polylogarithms, in “Structural Properties of Polylogarithms”, L., Lewin (ed.), Mathematical Surveys and Monographs (AMS), 37 (1991), 275–285.
[B-1] N., Bourbaki, ÉlÉments de MathÉmatique, AlgÉbre, Hermann, Paris 1962.
[B-2] N., Bourbaki, ÉlÉments de MathÉmatique, AlgÉbre Commutative, Hermann, Paris 1961.
[De0] P., Deligne, letter to Grothendieck, November 19, 1982.
[De1] P., Deligne, Théorie de Hodge, II, Publ. I.H.E.S., 40 (1971), 5–58.
[De2] P., Deligne, Le Groupe Fondamental de la Droite Projective Moins Trois Points, in “Galois group over ℚ” (Y., Ihara, K., Ribet, J.-P., Serre eds.), MSRI Publ. Vol. 16 (1989), 79–297.
[Dr] V. G., Drinfeld, On quasitriangular quasi-Hoph algebras and a group closely connected with Gal(ℚ/ℚ), Algebra i Analiz 2 (1990), 149–181; English translation: Leningrad Math. J. 2 (1991), 829–860.
[DW1] J.-C., Douai, Z., Wojtkowiak, On the Galois actions on the fundamental group of, Tokyo Journal of Math., 27 (2004), 21–34.
[DW2] J.-C., Douai, Z., Wojtkowiak, Descent for l-adic polylogarithms, Nagoya Math. J., 192 (2008), 59–88.
[F] H., Furusho, The multiple zeta value algebra and the stable derivation algebra, Publ. RIMS, Kyoto Univ. 39 (2003), 695–720.
[Ga] H., Gangl, Families of Functional Equations for Polylogarithms, Comtemp. Math. (AMS) 199 (1996), 83–105.
[Gol] K., Goldberg, The formal power series for Logexey, Duke Math. J., 23 (1956), 13–21.
[Gon] A. B., Goncharov, Galois symmetries of fundamental groupoids and noncommutative geometry, Duke Math. J., 128 (2005), 209–284.
[H] R., Hain, On a generalization of Hilbert's 21st problem, Ann. Scient. Éc. Norm. Sup., 19 (1986), 609–627.
[HM] R., Hain, M., Matsumoto, Weighted completion of Galois groups and Galois actions on the fundamental group of ℙ1 - {0, 1, ∞}, Compositio Math. 139 (2003), 119–167.
[Ih1] Y., Ihara, Braids, Galois groups, and some arithmetic functions, Proc. Intern. Congress of Math.Kyoto 1990, 99–120.
[Ih2] Y., Ihara, Some arithmetic aspects of Galois actions in the pro-p fundamental group of ℙ1 - {0, 1, ∞}, Proc. Symp. Pure Math. (AMS) 70 (2002) 247–273.
[Ii] S., Iitaka, Algebraic Geometry, Springer GTM 76 1982.
[K] V., Kurlin, The Baker–Campbell–Hausdorff formula in the free meta-abelian Lie algebra, J. of Lie Theory, 17 (2007), 525–538.
[La1] S., Lang, Fundamentals of Diophantine Geometry, Springer 1983.
[La2] S., Lang, Cyclotomic Fields I and II, GTM 121, Springer 1990.
[Le] L., Lewin, Polylogarithms and associated functions, North Holland, 1981.
[LS] P., Lochak, L., Schneps, A cohomological interpretation of the Grothendieck-Teichmüller group, Invent. math. 127 (1997), 571–600.
[MKS] W., Magnus, A., Karrass, D., Solitar, Combinatorial Group Theory, Second Revised Edition, Dover 1976.
[MS] W. G., McCallum and R. T., Sharifi, A cup product in the Galois cohomology of number fields, Duke Math. J., 120 (2003), 269–310.
[N0] H., Nakamura, Tangential base points and Eisenstein power series, in “Aspects of Galois Theory” (H., Völklein eds.), London Math. Soc. Lect. Note Ser., 256 (1999), 202–217.
[N1] H., Nakamura, Galois rigidity of pure sphere braid groups and profinite calculus, J. Math. Sci.Univ. Tokyo 1 (1994), 71–136.
[N2] H., Nakamura, Limits of Galois representations in fundamental groups along maximal degeneration of marked curves, I, Amer. J. Math. 121 (1999) 315–358; Part II, Proc. Symp. Pure Math. 70 (2002) 43–78.
[NW] H., Nakamura, Z., Wojtkowiak, On explicit formulae for l-adic polylogarithms, Proc. Symp. Pure Math. (AMS) 70 (2002) 285–294.
[NW2] H., Nakamura, Z., Wojtkowiak, in preparation.
[Ra] M., Raynaud, Propriétés de finitude du groupe fondamental, SGA7, Exposé II, Lect. Notes in Math.Springer, 288 (1972), 25–31.
[Rob] A., Robert, Elliptic Curves, Lect. Notes in Math. 326, Springer.
[Roq] P., Roquette, Einheiten und Divisorkalssen in endlich erzeugbaren Körpern, J. d. Deutschen Math. – Vereinigung, 60 (1957), 1–21.
[S1] Ch., Soulé, On higher p-adic regulators, Springer Lecture Notes in Math., 854 (1981), 372–401.
[S2] Ch., Soulé, Élements Cyclotomiques en K-ThÉorie, Ast'erisque, 147/148 (1987), 225–258.
[W0] Z., Wojtkowiak, The basic structure of polylogarithmic functional equations, in “Structural Properties of Polylogarithms”, L., Lewin (ed.), Mathematical Surveys and Monographs (AMS), 37 (1991), 205–231.
[W1] Z., Wojtkowiak, A note on functional equations of the p-adic polylogarithms, Bull. Soc. math. France, 119 (1991), 343–370.
[W2] Z., Wojtkowiak, Functional equations of iterated integrals with regular singularities, Nagoya Math. J., 142 (1996), 145–159.
[W3] Z., Wojtkowiak, Monodromy of iterated integrals and non-abelian unipotent periods, in “Geometric Galois Actions II”, London Math. Soc. Lect. Note Ser. 243 (1997) 219–289.
[W4] Z., Wojtkowiak, On ℓ-adic iterated integrals, I – Analog of Zagier Conjecture, Nagoya Math. J., 176 (2004), 113–158.
[W5] Z., Wojtkowiak, On ℓ-adic iterated integrals, II – Functional equations and ℓ-adic polylogarithms, Nagoya Math. J., 177 (2005), 117–153.
[W6] Z., Wojtkowiak, On ℓ-adic iterated integrals, III – Galois actions on fundamental groups, Nagoya Math. J., 178 (2005), 1–36.
[W7] Z., Wojtkowiak, On ℓ-adic iterated integrals, IV – ramification and generators of Galois actions on fundamental groups and torsors of paths, Math. J. Okayama Univ., 51 (2009), 47–69.
[W8] Z., Wojtkowiak, On the Galois actions on torsors of paths, I – Descent of Galois representations, J. Math. Univ. Tokyo., 14 (2007), 177–259.
[W9] Z., Wojtkowiak, A note on functional equations of ℓ-adic polylogarithms, J. Inst. Math. Jussieu, 3 (2004), 461–471.
[W10] Z., Wojtkowiak, On ℓadic Galois periods, relations between coefficients of Galois representations on fundamental groups of a projective line minus a finite number of points, Algèbre et théorie des nombres. Années 20072009, Proceedings of the Conference “l-adic Cohomology and Number Theory” held at Luminy, Marseille, (December 10–14, 2007), Publ. Math. Univ.Franche-Comté Besançon Algèbr. Theor. Nr., Lab. Math. Besançon, Besançon, 2009, pp. 157–174. (available at URL: Equipe/AlgebreTheorieDesNombres/pmb.html)
[Z] D., Zagier, Polylogarithms, Dedekind zeta functions and the algebraic Ktheory of Fields, in “Arithmetic Algebraic Geometry”, G., van der Geer et al.(eds.), Progress in Math., Birkhäuser, 89 (1991), 391–430.