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) Samir Siksek - University of Warwik,
Titre Elliptic curves over real quadratic fields are modular.
Date26/05/2014
Horaire14:00 à 16:00
Diffusion
RésumeWe combine recent breakthroughs in modularity lifting with a3-5-7 modularity switching argument to deduce modularity of ellipticcurves over real quadratic fields. We discuss the implications for theFermat equation. In particular we prove an asymptotic version ofFermat's Last Theorem over $\mathbf Q(\sqrt{d})$ for a subset of squarefreepositive~$d$ having density~5/6. This is based on joint work with NunoFreitas (Bayreuth) and Bao Le Hung (Harvard).
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