Abelian varieties over large algebraic fields with infinite torsion
Number Theory
2010-12-14 v1
Abstract
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.
Cite
@article{arxiv.1012.2477,
title = {Abelian varieties over large algebraic fields with infinite torsion},
author = {David Zywina},
journal= {arXiv preprint arXiv:1012.2477},
year = {2010}
}