The stable trace formula for Shimura varieties of abelian type

2021/10/11 by Mark Kisin, Sug Woo Shin, Kisin, Mark +3 · 1 citation
Mathematics · #11G15 #11G18 #14G35 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2110.05381

openalex publication_date 2021/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We express the Frobenius-Hecke traces on the compactly supported cohomology of a Shimura variety of abelian type in terms of elliptic parts of stable Arthur-Selberg trace formulas for the endoscopic groups. This confirms predictions of Langlands and Kottwitz at primes where the level is hyperspecial.

Citations

• Revêtements étales et groupe fondamental (SGA 1)
• Endoscopic Classification of Representations: Inner Forms of Unitary Groups
• Complexes d'intersection des compactifications de Baily-Borel. Le cas des groupes unitaires sur Q
• The stabilization of the Frobenius--Hecke traces on the intersection cohomology of orthogonal Shimura varieties

Cited by

• The cohomology of certain intermediate strata of Kottwitz varieties

Related

• The stabilization of the Frobenius--Hecke traces on the intersection cohomology of orthogonal Shimura varieties
• The cohomology of certain intermediate strata of Kottwitz varieties
• The trace formula and the existence of PEL type Abelian varieties modulo p
• Cohomologie d'intersection des variétés modulaires de Siegel, suite
• On the cohomology of certain non-compact Shimura varieties (with an appendix by Robert Kottwitz)