An automorphic description of the zeta function of the basic stratum of certain Kottwitz varieties

2024/11/02 by Liu, Yachen · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2411.01224

Abstract

We derive formulas for the number of points on the basic stratum of certain Kottwitz varieties in terms of automorphic representations and certain explicit polynomials, for which we present efficient algorithms for computation. We obtain our results using the trace formula, base change, 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.

Cited by

• The cohomology of certain intermediate strata of Kottwitz varieties

Related

• The cohomology of certain intermediate strata of Kottwitz varieties
• The basic stratum of some simple Shimura varieties
• Computing zeta functions over finite fields
• Shimura varieties with Γ₁(p)-level via Hecke algebra isomorphisms: the Drinfeld case
• Counting points on varieties over finite fields of small characteristic