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 (3)

• Revêtements étales et groupe fondamental (SGA 1)
• Endoscopic Classification of Representations: Inner Forms of Unitary Groups
• Le lemme fondamental pour l'endoscopie tordue: réduction aux éléments unités