Abelian obstructions in inverse Galois theory
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Théorie des Nombres et Algorithmique Arithmétique [A2X] | |
| dc.contributor.author | CADORET, Anna | |
| hal.structure.identifier | Laboratoire Paul Painlevé - UMR 8524 [LPP] | |
| dc.contributor.author | DÈBES, Pierre | |
| dc.date.issued | 2009 | |
| dc.identifier.issn | 0025-2611 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | Springer Verlag | |
| dc.title.en | Abelian obstructions in inverse Galois theory | |
| dc.type | Article de revue | |
| bordeaux.journal | Manuscripta mathematica | |
| bordeaux.page | à paraître | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00355720 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00355720v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Manuscripta%20mathematica&rft.date=2009&rft.spage=%C3%A0%20para%C3%AEtre&rft.epage=%C3%A0%20para%C3%AEtre&rft.eissn=0025-2611&rft.issn=0025-2611&rft.au=CADORET,%20Anna&D%C3%88BES,%20Pierre&rft.genre=article |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||