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arXiv · 1304.7161

Eisenstein classes, elliptic Soul\'e elements and the $\ell$-adic elliptic polylogarithm

Guido Kings
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Abstract

This is a completely rewritten version of the paper formerly entitled "Sheaves of Iwasawa modules, moment maps and the $\ell$-adic elliptic polylogarithm". The proof of the main result is also simplified. In the paper we study systematically the $\ell$-adic realization of the elliptic polylogarithm in the context of sheaves of Iwasawa modules. This leads to a description of the elliptic polylogarithm in terms of elliptic units. As an application we prove a precise relation between $\ell$-adic Eisenstein classes and elliptic Soul\'e elements. This allows to give a new proof of the formula for the residue of the $\ell$-adic Eisenstein classes at the cusps and reproves the formula for the cup-product construction in \cite{Huber-Kings99}. The paper is the elaboration of lectures given at the Pune-Workshop on the proof of the Bloch-Kato conjectures for the Riemann zeta function in 2012.

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Guido Kings. 2013-04-26. Eisenstein classes, elliptic Soul\'e elements and the $\ell$-adic elliptic polylogarithm. https://arxiv.org/abs/1304.7161

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