Formes modulaires surconvergentes, ramification et classicit\'e

TL;DR

This paper proves a classicality theorem for overconvergent modular forms on certain PEL Shimura varieties, extending previous results to cases without ramification using an analytic continuation approach.

Contribution

It generalizes classicality results to ramified PEL Shimura varieties of type (A) and (C) without ramification assumptions, employing an analytic continuation method.

Findings

Established classicality of overconvergent modular forms in new ramified settings

Extended analytic continuation techniques to broader Shimura varieties

Provided a framework for integral structures on rigid spaces

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.