Abelian subvarieties

Hendrik W. Lenstra, Frans Oort, Yuri G. Zarhin

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Let K be a field and let X be an abelian variety over K. The group Aut X of K-automorphisms of X acts in a natural way on the set of abelian subvarieties of X that are defined over K. In this paper it is proved that the number of orbits is finite. The proof makes use of a finiteness result about semisimple algebras.

Original languageEnglish (US)
Pages (from-to)513-516
Number of pages4
JournalJournal of Algebra
Volume180
Issue number2
DOIs
StatePublished - Mar 1996

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

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