Séminaires : Séminaire Théorie des Nombres

Equipe(s) : tn,
Responsables :Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos
Email des responsables : ziyang.gao@imj-prg.fr
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Orateur(s) O. Rizzo - ,
Titre Mazur's question on mod 11 representations of elliptic curves.
Date03/12/1998
Horaire14:00 à 16:00
Diffusion
RésumeGiven an integer N, we can naturally associate to each elliptic curveover Q a Galois representation mod N. Mazur asked if there existpairs of (non-isogenous) elliptic curves with isomorphic mod Nrepresentation. Using the geometry of a particular class of modularsurfaces introduced by Kani, which turns out to be a moduli space forMazur's problem, we prove that, for N=11, there are infinitely manysuch pairs (even if we cannot build a single example...)
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