Shimura varieties and twisted orbital integrals
type: Item
instance of: scholarly article
title: Shimura varieties and twisted orbital integrals
zbMATH Open document ID: 0533.14009
DOI: 10.1007/BF01450697
author: Robert Kottwitz
published in: Mathematische Annalen
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/163936
review text: Langlands' work on the Shimura varieties attached to quaternion algebras over totally real number fields led him to outline an attack on the problem of expressing the zeta function of a general Shimura variety in terms of automorphic L-functions. He divided his approach into parts, one of them being a combinatorial problem which arises during the comparison of the Selberg trace formula with the number of points on the Shimura variety over a finite field. The author of this paper shows that Langlands' combinatorial problem can be reduced to a standard problem in local harmonic analysis: that of establishing the spherical function identities needed for base change.
Mathematics Subject Classification ID: 14G10
Mathematics Subject Classification ID: 14G25
Mathematics Subject Classification ID: 11R80
Mathematics Subject Classification ID: 14K15
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F67
zbMATH DE Number: 3845737
zbMATH Keywords: twisted orbital integrals
zbMATH Keywords: zeta-function of Shimura variety
zbMATH Keywords: Langlands combinatorial problem
zbMATH Keywords: automorphic L-functions
MaRDI profile type: Publication
Wikidata QID: Q105717015
cites work: Reductive groups over a local field
cites work: Schemata over local rings. II
cites work: Orbital Integrals on GL 3
cites work: Rational conjugacy classes in reductive groups
cites work: Stable trace formula: Cuspidal tempered terms
cites work: Q4113939
cites work: Shimura Varieties and the Selberg Trace Formula
cites work: On the Zeta-Functions of Some Simple Shimura Varieties
cites work: Q3887686
cites work: Q3043304
cites work: Q5519950
OpenAlex ID: W2012221425
description: scientific article; zbMATH DE number 3845737