Galois Covers and the Hilbert-Grunwald Property

Pierre Dèbes[1]; Nour Ghazi[2]

  • [1] Université Lille 1 Laboratoire Paul Painlevé Mathématiques 59655 Villeneuve d’Ascq Cedex (France)
  • [2] Université Lille 1 Laboratoire Paul Painlevé Mathématiques 59655 Villeneuve d’Ascq Cedex (France) Université Lille 1 Laboratoire Paul Painlevé Mathématiques 59655 Villeneuve d’Ascq Cedex (France)

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 3, page 989-1013
  • ISSN: 0373-0956

Abstract

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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 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.

How to cite

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Dèbes, Pierre, and Ghazi, Nour. "Galois Covers and the Hilbert-Grunwald Property." Annales de l’institut Fourier 62.3 (2012): 989-1013. <http://eudml.org/doc/251131>.

@article{Dèbes2012,
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.},
affiliation = {Université Lille 1 Laboratoire Paul Painlevé Mathématiques 59655 Villeneuve d’Ascq Cedex (France); Université Lille 1 Laboratoire Paul Painlevé Mathématiques 59655 Villeneuve d’Ascq Cedex (France) Université Lille 1 Laboratoire Paul Painlevé Mathématiques 59655 Villeneuve d’Ascq Cedex (France)},
author = {Dèbes, Pierre, Ghazi, Nour},
journal = {Annales de l’institut Fourier},
keywords = {Inverse Galois theory; Grunwald’s problem; Hilbert’s irreducibility theorem; algebraic covers; local and global fields; Hurwitz spaces; Grunwald's problem; inverse Galois theory},
language = {eng},
number = {3},
pages = {989-1013},
publisher = {Association des Annales de l’institut Fourier},
title = {Galois Covers and the Hilbert-Grunwald Property},
url = {http://eudml.org/doc/251131},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Dèbes, Pierre
AU - Ghazi, Nour
TI - Galois Covers and the Hilbert-Grunwald Property
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 3
SP - 989
EP - 1013
AB - 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.
LA - eng
KW - Inverse Galois theory; Grunwald’s problem; Hilbert’s irreducibility theorem; algebraic covers; local and global fields; Hurwitz spaces; Grunwald's problem; inverse Galois theory
UR - http://eudml.org/doc/251131
ER -

References

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