@article{70b2feb3719d44da8d3f0dfc6ed947a7,
title = "Abelian subvarieties",
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.",
author = "Lenstra, {Hendrik W.} and Frans Oort and Zarhin, {Yuri G.}",
note = "Funding Information: We thank Mikhail Borovoi and Ke-Zheng Li for clarifying discussions. The third author is grateful for the hospitality enjoyed at the Mathematisch Instituut of the Universiteit Utrecht while work on this paper was being done. The first author was supported by NSF Grant DMS 92-24205. The first and third authors were supported by NWO, the Nederlandse Organisatie voor Wetenschappelijk Onderzoek.",
year = "1996",
month = mar,
doi = "10.1006/jabr.1996.0079",
language = "English (US)",
volume = "180",
pages = "513--516",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
number = "2",
}