Combinatorics of the basic stratum

TL;DR

This paper links the cohomology of a specific part of certain Shimura varieties to automorphic representations, providing a new perspective on their structure.

Contribution

It expresses the cohomology of the basic stratum of unitary Shimura varieties in terms of automorphic representations, offering a novel combinatorial approach.

Findings

Cohomology of the basic stratum is described via automorphic representations.

Provides a combinatorial framework for understanding Shimura varieties.

Connects geometric and automorphic aspects in number theory.

Abstract

We express the cohomology of the basic stratum of some unitary Shimura varieties associated to division algebras in terms of automorphic representations of the group in the Shimura datum.