Realisation de Hodge du polylogarithme d'un schema abelien

Details Realisation de Hodge du polylogarithme d'un schema abelien Realisation de Hodge du polylogarithme d'un schema abelien

2007-05-07

arxiv.org/abs/0705.0880v5

Mathematics

Algebraic Geometry

Appendice d'Andrey Levin ajoute

Scientific paper

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 $L$-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.

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