Bary-Soroker, Lior; Fehm, Arno; Wiese, Gabor Hilbertian fields and Galois representations. (English) Zbl 1410.12008 J. Reine Angew. Math. 712, 123-139 (2016). 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. Cited in 1 ReviewCited in 6 Documents MSC: 12E25 Hilbertian fields; Hilbert’s irreducibility theorem 12E30 Field arithmetic 20E18 Limits, profinite groups 20E22 Extensions, wreath products, and other compositions of groups PDFBibTeX XMLCite \textit{L. Bary-Soroker} et al., J. Reine Angew. Math. 712, 123--139 (2016; Zbl 1410.12008) Full Text: DOI arXiv