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Triviality of $X_{\mathrm{split}} (N) (Q )$ for certain congruence classes of the level

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorPARENT, Pierre
dc.date.accessioned2024-04-04T02:46:23Z
dc.date.available2024-04-04T02:46:23Z
dc.date.created2002
dc.date.issued2003
dc.identifier.issn0764-4442
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191546
dc.description.abstractEnWe give a criterion to check if, given a prime number N, the only rational points of the modular curve $X_{\mathrm{split}} (N)$ are trivial ({\it i.e.} cusps or points furnished by complex multiplication). We then prove that this criterion is verified for N large enough and satisfying explicit congruences.
dc.language.isoen
dc.publisherElsevier
dc.subjectpoints de Gross-Heegner
dc.subjectCourbes elliptiques
dc.subjectcourbes modulaires
dc.subjectpoints rationnels
dc.subjectreprésentations galoisiennes
dc.subjectpoints de Gross-Heegner.
dc.title.enTriviality of $X_{\mathrm{split}} (N) (Q )$ for certain congruence classes of the level
dc.typeArticle de revue
dc.subject.halMathématiques [math]/Théorie des nombres [math.NT]
bordeaux.journalComptes rendus de l'Académie des sciences. Série I, Mathématique
bordeaux.page377-380
bordeaux.volume5
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue336
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-00325667
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-00325667v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Comptes%20rendus%20de%20l'Acad%C3%A9mie%20des%20sciences.%20S%C3%A9rie%20I,%20Math%C3%A9matique&rft.date=2003&rft.volume=5&rft.issue=336&rft.spage=377-380&rft.epage=377-380&rft.eissn=0764-4442&rft.issn=0764-4442&rft.au=PARENT,%20Pierre&rft.genre=article


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