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) M. Kisin - ,
Titre Overconvergent Modular Forms and the Fontaine-Mazur conjecture
Date28/01/2002
Horaire14:00 à 16:00
Diffusion
RésumeThe Fontaine-Mazur conjecture predicts that 2-dimensional p-adicGaloisrepresentations, whose restriction to a decomposition group at p satisfiesa certaincondition (potential semi-stability), come from modular forms.I will explain a result which says that if a representation satisfiesthisconditionand comes from an overconvergent modular form, then it comes from aclassical modular form.This is significant, because overconvergent modular forms are very closelyrelatedto classical ones. The fact that the potential semi-stability conditioncan distinguishbetween classical and non-classical forms, therefore provides a goodtestof the conjecture.
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