On the characterization of Hilbertian fields

Abstract

The main goal of this work is to answer a question of P. D`ebes and D. Haran by relaxing the condition for Hilbertianity. Namely we prove that for a field K to be Hilbertian it suffices that K has the irreducible specialization property merely for absolutely irreducible polynomials.

(v2) contains a new application of the main result (v3) Changed the numbering of thms, lemmas, etc., to fit the published version

Cited by in corpus (1)

• Odoni's conjecture on arboreal Galois representations is false