%0 Journal Article
%T Les classes d'Eisenstein des varietes de Hilbert-Blumenthal
%A David Blotti¨¨re
%J Mathematics
%D 2007
%I arXiv
%X This article deals with the Eisenstein classes of Hilbert-Blumenthal families of abelian varieties. We first give a coordinate expression of these one at the topological level, using currents defined by Levin. Then we study the degeneration of these Eisenstein classes at a cusp of the Baily-Borel compactification of the Hilbert-Blumenthal variety. We show, using the explicit description of the Eisenstein classes obtained previously, that these classes degenerate in special values of an $L$-function associated to the underlying totally real number field. We deduce then both a geometric proof the Klingen-Siegel Theorem and a non vanishing result for some of these Eisenstein classes .
%U http://arxiv.org/abs/0706.2455v2