Displaying similar documents to “Algebraic covers : field of moduli versus field of definition”

Stable reduction of three point covers

Stefan Wewers (2005)

Journal de Théorie des Nombres de Bordeaux

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This note gives a survey of some recent results on the stable reduction of covers of the projective line branched at three points.

Galois Covers and the Hilbert-Grunwald Property

Pierre Dèbes, Nour Ghazi (2012)

Annales de l’institut Fourier

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