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Serre's uniformity problem in the split Cartan case

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorBILU, Yuri
hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPARENT, Pierre
dc.date.accessioned2024-04-04T02:39:54Z
dc.date.available2024-04-04T02:39:54Z
dc.date.created2009-03-02
dc.date.issued2011
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191017
dc.description.abstractEnWe prove that there exists an integer p_0 such that X_split(p)(Q) is made of cusps and CM-points for any prime p>p_0. Equivalently, for any non-CM elliptic curve E over Q and any prime p>p_0 the image of the Galois representation induced by the Galois action on the p-division points of E is not contained in the normalizer of a split Cartan subgroup. This gives a partial answer to an old question of Serre.
dc.language.isoen
dc.title.enSerre's uniformity problem in the split Cartan case
dc.typeArticle de revue
dc.identifier.doi10.4007/annals.2011.173.1.13
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
dc.subject.halMathématiques [math]/Géométrie algébrique [math.AG]
dc.identifier.arxiv0807.4954
bordeaux.journalAnn. Math. (II)
bordeaux.page569-584
bordeaux.volume173
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00383077
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00383077v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Ann.%20Math.%20(II)&rft.date=2011&rft.volume=173&rft.issue=1&rft.spage=569-584&rft.epage=569-584&rft.au=BILU,%20Yuri&PARENT,%20Pierre&rft.genre=article


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