Abelian varieties over large algebraic fields with infinite torsion

Details Abelian varieties over large algebraic fields with infinite torsion Abelian varieties over large algebraic fields with infinite torsion

2010-12-11

arxiv.org/abs/1012.2477v1

Mathematics

Number Theory

Scientific paper

Let A be an abelian variety of positive dimension defined over a number field K and let Kbar be a fixed algebraic closure of K. For each element sigma of the absolute Galois group Gal(Kbar/K), let Kbar(sigma) be the fixed field of sigma in Kbar. We shall prove that the torsion subgroup of A(Kbar(sigma)) is infinite for all sigma in Gal(Kbar/K) outside of some set of Haar measure zero. This proves the number field case of a conjecture of Geyer and Jarden from 1978.

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