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Descent for l-Adic Polylogarithms

Published online by Cambridge University Press:  11 January 2016

Jean-Claude Douai  and
Zdzisław Wojtkowiak
Jean-Claude Douai
Affiliation:
UFR de Mathématiques UMR AGAT CNRS Université des Sciences et Technologies de Lille, F-59655 Villeneuve d’Ascq Cedex, France, [email protected]
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, [email protected], UFR de Mathématiques UMR AGAT CNRS Université des Sciences et Technologies de Lille,F-59655 Villeneuve d’Ascq Cedex, France
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Abstract

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Let L be a finite Galois extension of a number field K. Let G:= Gal(L/K). Let z1,…, zN ∊ L* \ {1} and let m1 …, mN ∊ ℚl. Let us assume that the linear combination of l-adic polylogarithms (constructed in some given way) is a cocycle on GL and that the formal sum is G-invariant. Then we show that cn determines a unique cocycle sn on GK. We also prove a weak version of Zagier conjecture for l-adic dilogarithm. Finally we show that if c2 is “motivic” (m1,…, mN ∊ ℚ) then s2 is also “motivic”.

Keywords

11G55
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 192 , 2008 , pp. 59 - 88
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

References

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