3 papers
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…
math.NT2026
Integrally Hilbertian rings and the polynomial Schinzel hypothesis
Angelot Behajaina, Pierre Dèbes, Joachim König
The classical Hilbert specialization property is a field-theoretic tool ensuring that polynomial irreducibility over a field is preserved under specialization of some of the variab…
math.NT2025
Improvements on dimension growth results and effective Hilbert's irreducibility theorem
Raf Cluckers, Pierre Dèbes, Yotam I. Hendel +2
We sharpen and generalize the dimension growth bounds for the number of points of bounded height lying on an irreducible algebraic variety of degree , over any global field. In…