Galois Covers and the Hilbert-Grunwald Property
Annales de l'Institut Fourier, Volume 62 (2012) no. 3, pp. 989-1013.

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 . The general strategy is to study and exploit the good reduction of certain twisted models of the covers and of the associated moduli spaces.

Notre résultat principal mêle plusieurs thèmes  : il contient une conclusion de type Grunwald-Wang, une version du théorème d’irréductibilité de Hilbert et une forme p-adique à la Harbater, mais avec bonne réduction, du problème inverse de Galois sous sa forme régulière (RIGP). Nous en déduisons un énoncé qui pose de nouvelles questions sur le RIGP sur . La stratégie générale est d’étudier et d’exploiter la bonne réduction de certains modèles tordus de revêtements et des espaces de modules associés.

Received:
Accepted:
DOI: 10.5802/aif.2714
Classification: 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
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Dèbes, Pierre; Ghazi, Nour. Galois Covers and  the Hilbert-Grunwald Property. Annales de l'Institut Fourier, Volume 62 (2012) no. 3, pp. 989-1013. doi : 10.5802/aif.2714. https://aif.centre-mersenne.org/articles/10.5802/aif.2714/

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