Classicality for small slope overconvergent automorphic forms on some compact PEL Shimura varieties of type C

TL;DR

This paper establishes a small slope criterion for the classicality of overconvergent automorphic forms on certain compact PEL Shimura varieties of type C, extending previous work and advancing the cohomological approach.

Contribution

It generalizes Coleman's classicality criterion to higher-dimensional Shimura varieties using rigid cohomology of the ordinary locus.

Findings

Proves a small slope criterion for classicality of overconvergent forms.

Extends cohomological methods to higher-dimensional Shimura varieties.

Provides foundational work for further generalizations in automorphic forms theory.

Abstract

We study the rigid cohomology of the ordinary locus in some compact PEL Shimura varieties of type C with values in automorphic local systems and use it to prove a small slope criterion for classicality of overconvergent Hecke eigenforms. This generalises the work of Coleman, and is a first step in an ongoing project to extend the cohomological approach to classicality to higher-dimensional Shimura varieties.