Endomorphisms of abelian varieties over fields of finite characteristic

Ju G. Zarhin

doi:10.1070/IM1975v009n02ABEH001476

Endomorphisms of abelian varieties over fields of finite characteristic

Ju G. Zarhin

Mathematics

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

5 Scopus citations

Abstract

The semisimplicity of -adic representations corresponding to one-dimensional étale cohomology, and a proof of the Tate’s conjecture about homomorphisms of abelian varieties, are derived from the Tate’s finiteness conjecture on isogenies of polarized abelian varieties.

Original language	English (US)
Pages (from-to)	255-260
Number of pages	6
Journal	Mathematics of the USSR - Izvestija
Volume	9
Issue number	2
DOIs	https://doi.org/10.1070/IM1975v009n02ABEH001476
State	Published - Apr 30 1975

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1070/IM1975v009n02ABEH001476

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title = "Endomorphisms of abelian varieties over fields of finite characteristic",

abstract = "The semisimplicity of -adic representations corresponding to one-dimensional {\'e}tale cohomology, and a proof of the Tate{\textquoteright}s conjecture about homomorphisms of abelian varieties, are derived from the Tate{\textquoteright}s finiteness conjecture on isogenies of polarized abelian varieties.",

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Endomorphisms of abelian varieties over fields of finite characteristic

Abstract

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