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 -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 -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.
@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},
volume = {62},
year = {2012},
pages = {989-1013},
doi = {10.5802/aif.2714},
zbl = {1255.14022},
mrnumber = {3013814},
language = {en},
url = {http://dml.mathdoc.fr/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) pp. 989-1013. doi : 10.5802/aif.2714. http://gdmltest.u-ga.fr/item/AIF_2012__62_3_989_0/
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