Formes modulaires surconvergentes, ramification et classicit\'e

Abstract

We prove in this paper a classicality result for overconvergent modular forms on PEL Shimura varieties of type (A) or (C), without any ramification hypothesis. We use an analytic continuation method, which generalizes previous results in the unramified setting. We work with the rational model of the Shimura variety, and use an embedding into the Siegel variety to define the integral structures on the rigid space.