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.
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Journal für die reine und angewandte Mathematik is the oldest mathematics periodical still in existence. Founded in 1826 by August Leopold Crelle and edited by him until his death in 1855, it soon became widely known under the name of
Crelle’s Journal. In the 190 years of its existence,
Crelle’s Journal has developed to an outstanding scholarly periodical with one of the worldwide largest circulations among mathematics journals.