Galois Covers and the Hilbert-Grunwald Property  [ Revêtements galoisiens et propriété de Hilbert-Grunwald ]
Annales de l'Institut Fourier, Tome 62 (2012) no. 3, p. 989-1013
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.
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.
DOI : https://doi.org/10.5802/aif.2714
Classification:  14H30,  11R32,  12F12,  12E25,  14Gxx,  14Dxx,  14H10
Mots clés: théorie inverse de Galois, problème de Grunwald, théorème d’irréductibilité de Hilbert, revêtements algébriques, corsp locaux, corps globaux, espaces de Hurwitz
@article{AIF_2012__62_3_989_0,
     author = {D\`ebes, Pierre and Ghazi, Nour},
     title = {Galois Covers and  the Hilbert-Grunwald Property},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {62},
     number = {3},
     year = {2012},
     pages = {989-1013},
     doi = {10.5802/aif.2714},
     mrnumber = {3013814},
     zbl = {1255.14022},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2012__62_3_989_0}
}
Dèbes, Pierre; Ghazi, Nour. Galois Covers and  the Hilbert-Grunwald Property. Annales de l'Institut Fourier, Tome 62 (2012) no. 3, pp. 989-1013. doi : 10.5802/aif.2714. http://www.numdam.org/item/AIF_2012__62_3_989_0/

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