Torsion of abelian varieties over large algebraic fields

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 A l( K ̃ (σ))≠0 . Here K̃ denotes the algebraic closure of K and K ̃ (σ) the fixed field in K̃ of σ. The expression “almost all σ” means “all but a set of σ of Haar measure 0”.