Cohomology of fiber systems and Mordell-Weil groups of abelian varieties
type: Item
instance of: scholarly article
title: Cohomology of fiber systems and Mordell-Weil groups of abelian varieties
zbMATH Open document ID: 0645.14019
DOI: 10.1215/S0012-7094-88-05603-7
author: Alice Silverberg
published in: Duke Mathematical Journal
publication date: 1988-01-01T00:00:00Z
review text: Given a real semisimple Lie group \(G\) with an arithmetic subgroup \(\Gamma\) and a representation of \(G\) in a symplectic vector space \(V\), one obtains a fiber system of abelian varieties over \(\Delta =D/\Gamma\), where \(D\) is the Hermitian symmetric domain associated to \(G\). The generic fiber being denoted by \(A\), it is shown that the Mordell-Weil group \(A(\mathbb C(\Delta))\) is finite if \(H^0(\Gamma,V)\) and \(H^1(\Gamma,V)\) are trivial.
Mathematics Subject Classification ID: 11G18
Mathematics Subject Classification ID: 11F75
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14K10
Mathematics Subject Classification ID: 22E40
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 32L10
zbMATH DE Number: 4051788
zbMATH Keywords: fiber system of abelian varieties
zbMATH Keywords: Mordell-Weil group
reviewed by: J. H. de Boer
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4051788