Endomorphisms and torsion of Abelian varieties
type: Item
instance of: scholarly article
title: Endomorphisms and torsion of Abelian varieties
zbMATH Open document ID: 0632.14035
DOI: 10.1215/S0012-7094-87-05410-X
published in: Duke Mathematical Journal
publication date: 1987-01-01T00:00:00Z
review text: It is proved the following result which is a final solution of the torsion problem for abelian varieties A over the maximal abelian extension \(K^{ab}\) of a given number field K. Let A be K-isogenous to the product \(X_ 1\times...\times X_ n\) of simple abelian varieties \(X_ i\) over K. Then the torsion subgroup \(A(K^{ab})_{tors}\) is finite iff all \(X_ i\) are not of CM-type over K (1\(\leq i\leq h)\). For CM-type A we have \(A(K^{ab})_{tors}=A(\bar K)_{tors}\) where \(\bar K\) is the algebraic closure of K.
Mathematics Subject Classification ID: 14K05
zbMATH DE Number: 4027668
zbMATH Keywords: solution of the torsion problem for abelian varieties
author: Yu. G. Zarhin
reviewed by: A. N. Parshin
MaRDI profile type: Publication
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full work available at URL: s0012-7094-87-05410-x
OpenAlex ID: W2071435108
description: scientific article; zbMATH DE number 4027668