Hilbertian fields and Galois representations
  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. 
Lior Bary-Soroker and Arno Fehm and Gabor Wiese
math.NT math.GR