Realisation de Hodge du polylogarithme d'un schema abelien
Abstract
The main result of this article is the fact that the currents defined by Levin give a description of the polylogarithm of an abelian scheme at the topological level. This result was a conjecture of Levin. This provides a method to explicit the Eisenstein classes of an abelian scheme at the topological level. These classes are of special interest since they have a motivic origin by a theorem of Kings. In a forthcoming article, we use the main result of this paper to prove that the Eisenstein classes of the universal abelian scheme over an Hilbert-Blumenthal variety degenerate at the boundary of the Baily-Borel compactification of the base in a special value of an -function associated to the underlying totally real number field. As a corollary, we get a non vanishing result for some of these Eisenstein classes in this geometric situation.
Cite
@article{arxiv.0705.0880,
title = {Realisation de Hodge du polylogarithme d'un schema abelien},
author = {David Blottiere},
journal= {arXiv preprint arXiv:0705.0880},
year = {2008}
}