Abelian obstructions in inverse Galois theory

Cadoret, Anna; Dèbes, Pierre

Document type :

Article dans une revue scientifique: Article original

Title :

Abelian obstructions in inverse Galois theory

Author(s) :

Cadoret, Anna [Auteur]
Théorie des Nombres et Algorithmique Arithmétique [A2X]
Institut de Mathématiques de Bordeaux [IMB]
Dèbes, Pierre [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Manuscripta mathematica

Pages :

à paraître

Publisher :

Springer Verlag

Publication date :

2009

ISSN :

0025-2611

English abstract : [en]

We show that if a ﬁnite group G is the Galois group of a Galois cover of P1 over Q, then the orders pn of the abelianization of its p-Sylow subgroups are bounded in terms of their index m, of the branch point number r and ...
Show more >We show that if a ﬁnite group G is the Galois group of a Galois cover of P1 over Q, then the orders pn of the abelianization of its p-Sylow subgroups are bounded in terms of their index m, of the branch point number r and the smallest prime ℓ ̸| |G| of good reduction of the branch divisor. This is a new constraint for the regular inverse Galois problem: if pn is suitably large compared to r and m, the branch points must coalesce modulo small primes. We further conjecture that pn should be bounded only in terms of r and m. We use a connection with some rationality question on the torsion of abelian varieties. For example, our conjecture follows from the so-called torsion conjectures. Our approach also provides a new viewpoint on Fried's Modular Tower program and a weak form of its main conjecture.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

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