Les classes d'Eisenstein des varietes de Hilbert-Blumenthal
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Publication:3396252
DOI10.1093/IMRN/RNP051zbMath1214.11058arXiv0706.2455OpenAlexW2142928939MaRDI QIDQ3396252
Publication date: 16 September 2009
Published in: Unnamed Author (Search for Journal in Brave)
Abstract: 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 .
Full work available at URL: https://arxiv.org/abs/0706.2455
Modular and Shimura varieties (14G35) Polylogarithms and relations with (K)-theory (11G55) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)
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