Conjugation of Kuga fiber varieties
type: Item
instance of: scholarly article
title: Conjugation of Kuga fiber varieties
zbMATH Open document ID: 0758.14028
DOI: 10.1007/BF01934323
author: Salman Abdulali
published in: Mathematische Annalen
publication date: 1993-01-12T00:00:00Z
full work available at URL: https://eudml.org/doc/164999
review text: A Kuga fiber variety is a family of abelian varieties parametrized by an arithmetic variety and constructed from a symplectic representation of an algebraic group. A lower bound for the field of definition of a complex algebraic variety \(X\) is given by Bot\(X\), the strong bottom field; this is a field \(k\) such that for any automorphism \(\sigma\) of \(\mathbb{C}\), \(X^ \sigma\cong X\) if and only if \(\sigma\) is the identity on \(k\). The principal result of this paper is that if \(A\to V\) is a Kuga fiber variety defined by a \(\mathbb{Q}\)-irreducible representation satisfying a certain rigidity condition, and if the generic fibers are principal abelian varieties, then Bot\(A\) is an abelian extension of Bot\(V\). In fact, the Galois group of Bot\(A\) over Bot\(V\) is embedded into the class group of a maximal order in a simple algebra.
reviewed by: Salman Abdulali
Mathematics Subject Classification ID: 14K05
Mathematics Subject Classification ID: 14A05
Mathematics Subject Classification ID: 11G18
Mathematics Subject Classification ID: 14G35
zbMATH DE Number: 86197
zbMATH Keywords: Kuga fiber variety
zbMATH Keywords: arithmetic variety
zbMATH Keywords: field of definition
zbMATH Keywords: strong bottom field
zbMATH Keywords: class group of a maximal order
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 86197