Classicit\'e de formes modulaires surconvergentes

TL;DR

This paper proves a classicality theorem for overconvergent modular forms on certain PEL Shimura varieties using analytic continuation, extending understanding of modular forms in p-adic geometry.

Contribution

It establishes a classicality result for overconvergent modular forms on PEL Shimura varieties of type (A) or (C), employing the analytic continuation method.

Findings

Proves classicality of overconvergent modular forms on specified Shimura varieties.

Utilizes the analytic continuation method originally developed by Buzzard and Kassaei.

Extends classicality results to new types of PEL Shimura varieties.

Abstract

We prove in this paper a classicality result for overconvergent modular forms on PEL Shimura varieties of type (A) or (C) associated to an unramified reductive group on $\mathbb{Q}_p$. To get this result, we use the analytic continuation method, first used by Buzzard and Kassaei.