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Periods of Mixed Tate Motives, Examples, l-adic Side

  • Zdzisłlaw WojtkowiakEmail author
Conference paper
Part of the Progress in Mathematics book series (PM, volume 304)

Abstract

One hopes that the ℚ-algebra of periods of mixed Tate motives over SpecZ is generated by values of iterated integrals on ℙ1(ℂ) \ {0, 1,8} of sequences of one-forms dz⁄z and dz⁄z-1 from ⃗ 01 to⃗ 10. These numbers are also called multiple zeta values. In this note, assuming motivic formalism, we give a proof, that the ℚ-algebra of periods of mixed Tate motives over SpecZ is generated by linear combinations with rational coefficients of iterated integrals on ℙ1(ℂ) \ {0, 1,-1,8} of sequences of one-forms dz⁄z , dz⁄z -1 and dz⁄z +1 from ⃗ 01 to⃗ 10, which are unramified everywhere. The main subject of the paper is however the l-adic Galois analogue of the above result. We shall also discuss some other examples in thel-adic Galois setting.

Keywords

Fundamental group ??-adic polylogarithms periods mixed Tate motives Galois representations on fundamental groups Lie algebras Kummer characters 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Laboratoire Jean Alexandre Dieudonné, U.R.A. au C.N.R.S., N° 168 Département de MathématiquesUniversité de Nice-Sophia AntipolisNice Cedex 2France
  2. 2.Laboratoire Paul Painlevé U.M.R. C.N.R.S. N° 8524 U.F.R. de MathématiquesUniversité des Sciences et Technologies de LilleVilleneuve d’Ascq CedexFrance

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