Classicité de formes modulaires surconvergentes

Abstract

Nous généralisons le critère de classicité de formes modulaires surconvergentes sur les courbes modulaires dû à Coleman à certaines variétés de Shimura PEL de type (A) et~(C) associées à des groupes réductifs non ramifiés sur $\mathbb{Q}_p$. Notre démonstration s’inspire de la méthode de prolongement analytique de Buzzard et Kassaei. \vspace*4pt
We generalize Coleman classicity criterion for overconvergent modular forms on modular curves to the case of some PEL Shimura variety of type (A) or (C) associated to a reductive group unramified over $\mathbb{Q}_p$. Our demonstration is inspired by the analytic continuation method of Buzzard and Kassaei.

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Authors

Stéphane Bijakowski

Université Paris 13, LAGA, Villetaneuse, France

Current address:

Imperial College, London, UK Vincent Pilloni

CNRS, ENS Lyon, UMPA, Lyon, France

Benoît Stroh

CNRS, Université Paris 13, LAGA, Villetaneuse, France