The stable trace formula for Shimura varieties of abelian type

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.

References in corpus (7)

• 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
• Extending torsors on the punctured Spec(A_inf)
• Le lemme fondamental pour l'endoscopie tordue: réduction aux éléments unités
• Global L-packets of quasisplit $GSp(2n)$ and $GO(2n)$

Cited by in corpus (3)

• Sato-Tate Equidistribution for Families of Automorphic Representations through the Stable Trace Formula
• Galois representations for even general special orthogonal groups
• Mod $p$ points on Shimura varieties of parahoric level (with an appendix by Rong Zhou)