Endomorphisms of abelian varieties and points of finite order in characteristic p

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Abstract

An analog of the Tate hypothesis on homomorphisms of Abelian varieties is proved, in which points of sufficiently large prime order figure in place of the Tate modules. As is the case with the Tate hypothesis, this assertion follows formally from a finiteness hypothesis for isogenies of Abelian varieties, which is proved in characteristic p > 2 and for finite fields. The same methods are used to prove the finiteness of the set of Abelian varieties of a given dimension over a finite field.

Original languageEnglish (US)
Pages (from-to)415-419
Number of pages5
JournalMathematical Notes of the Academy of Sciences of the USSR
Volume21
Issue number6
DOIs
StatePublished - Jun 1 1977

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Abelian Variety
Endomorphisms
Finiteness
Galois field
Isogenies
Homomorphisms
Assertion
Figure
Analogue
Module

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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