Torsion of abelian varieties over large algebraic fields

Wulf Dieter Geyer, Moshe Jarden

Research output: Contribution to journalArticlepeer-review

Abstract

We prove: Let A be an abelian variety over a number field K. Then K has a finite Galois extension L such that for almost all σ∈Gal(L) there are infinitely many prime numbers l with Al(K̃(σ))≠0.Here K̃ denotes the algebraic closure of K and K̃(σ) the fixed field in K̃ of σ. The expression "almost all σ" means "all but a set of σ of Haar measure 0".

Original languageEnglish
Pages (from-to)123-150
Number of pages28
JournalFinite Fields and Their Applications
Volume11
Issue number1
DOIs
StatePublished - Jan 2005

Keywords

  • Linear algebraic groups
  • Mumford-Tate group
  • Torsion of abelian varieties

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