Isogenies of abelian varieties
type: Item
instance of: scholarly article
title: Isogenies of abelian varieties
zbMATH Open document ID: 0832.14034
DOI: 10.1016/0022-4049(93)90133-E
published in: Journal of Pure and Applied Algebra
publication date: 1994-03-10T00:00:00Z
review text: This paper deals with the following problems: Given two polarized abelian varieties \(X\) and \(Y\) over a field \(F\) which are isogenous over \(\overline F\), are they isogenous over \(F\)? And if they are not, how much of the \(n\)-torsion must be adjoined to \(F\) in order that they are? It is known that it suffices to adjoin all of the \(n\)-torsion for an integer \(n\) which is prime to \(\text{char} (F)\) and \(\geq 3\). The paper gives conditions on subgroups of the torsion which ensure that after adjoining this torsion to the field there exists an isogeny over this field.
Mathematics Subject Classification ID: 14K02
zbMATH DE Number: 500596
zbMATH Keywords: isogenous polarized abelian varieties
author: Alice Silverberg
author: Yu. G. Zarhin
reviewed by: Gerard van der Geer
MaRDI profile type: Publication
cites work: Abelian Varieties Over Function Fields
cites work: Q3663443
cites work: Q5597385
cites work: Q3849064
cites work: Fields of definition for homomorphisms of abelian varieties
cites work: Q5795562
cites work: Q5553838
cites work: Q3218239
full work available at URL: 0022-4049(93)90133-e
OpenAlex ID: W2068937418
description: scientific article; zbMATH DE number 500596