Abelian subvarieties

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

doi:10.1006/jabr.1996.0079

Abelian subvarieties

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

Mathematics

Research output: Contribution to journal › Article › peer-review

13 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 language	English (US)
Pages (from-to)	513-516
Number of pages	4
Journal	Journal of Algebra
Volume	180
Issue number	2
DOIs	https://doi.org/10.1006/jabr.1996.0079
State	Published - Mar 1996

All Science Journal Classification (ASJC) codes

Algebra and Number Theory

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10.1006/jabr.1996.0079

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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",

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TY - JOUR

T1 - Abelian subvarieties

AU - Lenstra, Hendrik W.

AU - Oort, Frans

AU - Zarhin, Yuri G.

N1 - 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.

PY - 1996/3

Y1 - 1996/3

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/0030094243

UR - https://www.scopus.com/pages/publications/0030094243#tab=citedBy

U2 - 10.1006/jabr.1996.0079

DO - 10.1006/jabr.1996.0079

M3 - Article

AN - SCOPUS:0030094243

SN - 0021-8693

VL - 180

SP - 513

EP - 516

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Abelian subvarieties

Abstract

All Science Journal Classification (ASJC) codes

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