Automorphic congruences and torsion in the cohomology of a simple unitary Shimura variety

TL;DR

This paper develops a flexible method to construct torsion cohomology classes in certain Shimura varieties and demonstrates their connection to infinitely many automorphic representations that are non-isomorphic yet weakly congruent.

Contribution

It introduces a new process for constructing torsion classes and establishes a link between these classes and a vast family of automorphic representations.

Findings

Constructed torsion cohomology classes in Shimura varieties.

Proved existence of infinitely many automorphic representations associated with torsion classes.

Showed these automorphic representations are non-isomorphic and weakly congruent.

Abstract

We first give a relative flexible process to construct torsion cohomology classes for Shimura varieties of Kottwitz-Harris-Taylor type with coefficient in a non too regular local system. We then prove that associated to each torsion cohomology class, there exists a infinity of irreducible automorphic representations in characteristic zero, which are pairwise non isomorphic and weakly congruent.