Torsion in the Coherent Cohomology of Shimura Varieties and Galois Representations

TL;DR

This paper presents a new method to generate congruences between Hecke eigenclasses, including torsion classes, in the coherent cohomology of automorphic vector bundles on Shimura varieties, utilizing generalized Hasse invariants.

Contribution

It introduces a novel approach for producing congruences in the coherent cohomology of Shimura varieties using generalized Hasse invariants and Ekedahl-Oort stratification.

Findings

Established a method for congruences involving torsion classes.

Applied generalized Hasse invariants to Shimura varieties.

Enhanced understanding of Galois representations via cohomological congruences.

Abstract

We introduce a method for producing congruences between Hecke eigenclasses, possibly torsion, in the coherent cohomology of automorphic vector bundles on certain good reduction Shimura varieties. The congruences are produced using some "generalized Hasse invariants" adapted to the Ekedahl-Oort stratification of the special fiber.