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Réalisation de Hodge du polylogarithme d'un schéma abélien et dégénérescence des classes d'Eisenstein des familles modulaires de Hilbert-Blumenthal.

Abstract : The Hodge realization of the polylogarithm of a complex abelian scheme of dimension g is a (2g-1)-extension of Hodge modules. When the abelian scheme is principally polarized, we describe the underlying topological extension by using currents of Green type introduced by Levin. Then, we apply this result to the Hilbert-Blumenthal modular families to show that some of these Eisenstein classes (built from the polylogarithm and a torsion section) degenerate, at infinity, in a special value of a L-function of the underlying totally real number field. This has two consequences: a partial version of the Klingen-Siegel theorem and a non vanishing
result for some of these Eisenstein classes. So, we prove that for any integer g greater than 2, there exists an abelian scheme of dimension g such that some of its Eisenstein classes are non zero.
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https://tel.archives-ouvertes.fr/tel-00132405
Contributor : David Blottière <>
Submitted on : Wednesday, February 21, 2007 - 12:35:39 PM
Last modification on : Wednesday, April 28, 2021 - 6:45:33 PM
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  • HAL Id : tel-00132405, version 1

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David Blottière. Réalisation de Hodge du polylogarithme d'un schéma abélien et dégénérescence des classes d'Eisenstein des familles modulaires de Hilbert-Blumenthal.. Mathématiques [math]. Université Paris-Nord - Paris XIII, 2006. Français. ⟨tel-00132405⟩

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