The cohomology of certain intermediate strata of Kottwitz varieties

2025/07/05 by Liu, Yachen
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2507.04122

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.

Citations

• An automorphic description of the zeta function of the basic stratum of certain Kottwitz varieties
• The stable trace formula for Shimura varieties of abelian type
• Equidistribution in supersingular Hecke orbits
• Combinatorics of the basic stratum
• The trace formula and the existence of PEL type Abelian varieties modulo p
• The basic stratum of some simple Shimura varieties
• The supersingular locus of the Shimura variety of GU(1,n-1) II
• On the cohomology of certain non-compact Shimura varieties (with an appendix by Robert Kottwitz)
• The supersingular locus of the Shimura variety for GU(1,s)

Related

• On the cohomology of certain non-compact Shimura varieties (with an appendix by Robert Kottwitz)
• On subquotients of the etale cohomology of Shimura varieties
• An automorphic description of the zeta function of the basic stratum of certain Kottwitz varieties
• The stable trace formula for Shimura varieties of abelian type
• On the \ mathbb F_l-cohomology of a simple unitary Shimura\n variety