CADORET, Anna; DÈBES, Pierre

Metadatos

Mostrar el registro completo del ítem

Licencia de uso del documento

CADORET, Anna
Institut de Mathématiques de Bordeaux [IMB]
Théorie des Nombres et Algorithmique Arithmétique [A2X]

DÈBES, Pierre
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Idioma

Article de revue

Este ítem está publicado en

Manuscripta mathematica. 2009p. à paraître

Springer Verlag

Resumen en inglés

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.< Leer menos

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251