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Journal de Th´ eorie des Nombres de Bordeaux

17

(2005), 271–282

Galois covers of P

1

over Q with prescribed local or global behavior by specialization

par Bernat PLANS et N´ uria VILA

R´esum´e. On consid`ere des versions raffin´ees du Probl`eme Inverse de Galois. Nous ´etudions le comportement local et global des sp´ecialisations rationnelles de quelques revˆetements galoisiens finis deP1Q.

Abstract. This paper considers some refined versions of the In- verse Galois Problem. We study the local or global behavior of rational specializations of some finite Galois covers ofP1Q.

BernatPlans

Dept. de Matem`atica Aplicada I Universitat Polit`ecnica de Catalunya Av. Diagonal, 647

08028 Barcelona, Spain E-mail:[email protected]

uriaVila

Dept. d’ `Algebra i Geometria Universitat de Barcelona

Gran Via de les Corts Catalanes, 585 08007 Barcelona, Spain

E-mail:[email protected]

Research partially supported by MCYT grant BFM2003-01898.

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