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hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
hal.structure.identifierThéorie des Nombres et Algorithmique Arithmétique [A2X]
dc.contributor.authorCADORET, Anna
hal.structure.identifierLaboratoire Paul Painlevé - UMR 8524 [LPP]
dc.contributor.authorDÈBES, Pierre
dc.date.issued2009
dc.identifier.issn0025-2611
dc.description.abstractEnWe 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.
dc.language.isoen
dc.publisherSpringer Verlag
dc.title.enAbelian obstructions in inverse Galois theory
dc.typeArticle de revue
bordeaux.journalManuscripta mathematica
bordeaux.pageà paraître
bordeaux.peerReviewedoui
hal.identifierhal-00355720
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00355720v1
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