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Pierre Dèbes; Nour Ghazi
Galois Covers and the Hilbert-Grunwald Property
(Revêtements galoisiens et propriété de Hilbert-Grunwald)
Annales de l'institut Fourier, 62 no. 3 (2012), p. 989-1013
Article: subscription required (your ip address: 54.82.17.138) | Reviews MR 3013814 | Zbl 1255.14022
Class. Math.: 14H30, 11R32, 12F12, 12E25, 14Gxx, 14Dxx, 14H10
Keywords: Inverse Galois theory, Grunwald’s problem, Hilbert’s irreducibility theorem, algebraic covers, local and global fields, Hurwitz spaces

Résumé - Abstract

Our main result combines three topics: it contains a Grunwald-Wang type conclusion, a version of Hilbert’s irreducibility theorem and a $p$-adic form à la Harbater, but with good reduction, of the Regular Inverse Galois Problem. As a consequence we obtain a statement that questions the RIGP over $\mathbb{Q}$. The general strategy is to study and exploit the good reduction of certain twisted models of the covers and of the associated moduli spaces.

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