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math.NT2026
Integral Specializations of Polynomials: Hilbert Irreducibility, Coprimality, and Density
Angelot Behajaina, Pierre Dèbes, Martin Widmer
The Hilbert specialization property of a field, whereby irreducibility of polynomials is preserved under specialization of some of the variables, admits an integral counterpart whe…
math.NT2026
Hurwitz spaces and Inverse Galois Theory
Pierre Dèbes
Hurwitz spaces which parametrize branched covers of the line play a prominent role in inverse Galois theory. This paper surveys fifty years of works in this direction with emphasis…