Hilbertian fields and Galois representations

Abstract

We prove a new Hilbertianity criterion for fields in towers whose steps are Galois with Galois group either abelian or a product of finite simple groups. We then apply this criterion to fields arising from Galois representations. In particular we settle a conjecture of Jarden on abelian varieties.

arXiv comment18 pages, accepted for publication in Journal für die reine und angewandte Mathematik