The cohomology of certain intermediate strata of Kottwitz varieties

TL;DR

This paper provides explicit formulas for Frobenius-Hecke traces on the etale cohomology of specific strata in Kottwitz varieties, linking automorphic representations with point counts via advanced trace formulas.

Contribution

It introduces new explicit formulas connecting automorphic representations and cohomological traces for certain Shimura variety strata, extending Kottwitz's point counting methods.

Findings

Explicit formulas for Frobenius-Hecke traces derived

Connections established between automorphic representations and cohomology

Enhanced understanding of Kottwitz varieties' cohomological structure

Abstract

We derive explicit formulas for the Frobenius-Hecke traces of the etale cohomology of certain strata of Kottwitz varieties (which are certain compact unitary type Shimura varieties considered by Kottwitz), in terms of automorphic representations and certain explicit polynomials. We obtain our results using the trace formula, representations of general linear groups over p-adic fields, and a truncation of the formula of Kottwitz for the number of points on Shimura varieties over finite fields.