Abelian obstructions in inverse Galois theory
CADORET, Anna
Institut de Mathématiques de Bordeaux [IMB]
Théorie des Nombres et Algorithmique Arithmétique [A2X]
Institut de Mathématiques de Bordeaux [IMB]
Théorie des Nombres et Algorithmique Arithmétique [A2X]
CADORET, Anna
Institut de Mathématiques de Bordeaux [IMB]
Théorie des Nombres et Algorithmique Arithmétique [A2X]
< Réduire
Institut de Mathématiques de Bordeaux [IMB]
Théorie des Nombres et Algorithmique Arithmétique [A2X]
Langue
en
Article de revue
Ce document a été publié dans
Manuscripta mathematica. 2009p. à paraître
Springer Verlag
Résumé en anglais
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 ...Lire la suite >
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.< Réduire
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