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Hilbertian fields and Galois representations. (English) Zbl 1410.12008

Summary: 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.

MSC:

12E25 Hilbertian fields; Hilbert’s irreducibility theorem
12E30 Field arithmetic
20E18 Limits, profinite groups
20E22 Extensions, wreath products, and other compositions of groups
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