Torsion of Abelian varieties of finite characteristic

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The finiteness of the torsion of Abelian varieties with a complete real field of endomorphisms in the maximal Abelian extension of the field of definition is proven. This assertion is formally deduced from the finiteness hypothesis for isogenic Abelian varieties, proven for characteristic p > 2. The structure is studied of the Lie algebra of Galois groups acting in a Tate module; in particular, for fields of characteristic greater than two there is proven one-dimensionality of the center of the Lie algebra.

Original languageEnglish (US)
Pages (from-to)493-498
Number of pages6
JournalMathematical Notes of the Academy of Sciences of the USSR
Volume22
Issue number1
DOIs
StatePublished - Jul 1 1977

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Abelian Variety
Torsion
Finiteness
Lie Algebra
Galois group
Endomorphisms
Assertion
Dimensionality
Module

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Torsion of Abelian varieties of finite characteristic. / Zarkhin, Yuriy G.

In: Mathematical Notes of the Academy of Sciences of the USSR, Vol. 22, No. 1, 01.07.1977, p. 493-498.

Research output: Contribution to journalArticle

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