On the motive of a reductive group
type: Item
instance of: scholarly article
title: On the motive of a reductive group
zbMATH Open document ID: 0904.11014
published in: Inventiones Mathematicae
publication date: 1997-12-10T00:00:00Z
review text: Following Steinberg, a motive \(M\) of Artin-Tate type is attached to any connected reductive group \(G\) over a field \(k.\) When \(k\) is a local field of characteristic 0, the \(L\)-function \(L(M)\) is finite if and only if Serre's Euler-Poincaré measure of \(G(k)\) is non-zero. In this case, a local function equation is obtained. When \(k\) is a number field, \(L(M)\) is used to evaluate certain adélic integrals in the trace formula.
Mathematics Subject Classification ID: 11G40
Mathematics Subject Classification ID: 14A20
Mathematics Subject Classification ID: 11G09
Mathematics Subject Classification ID: 20G30
Mathematics Subject Classification ID: 20G35
zbMATH DE Number: 1096053
zbMATH Keywords: motive of Artin-Tate type
zbMATH Keywords: connected reductive group
zbMATH Keywords: \(L\)-function
zbMATH Keywords: number field
author: Benedict H. Gross
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
full work available at URL: s002220050186
OpenAlex ID: W2034737772
DOI: 10.1007/S002220050186
description: scientific article; zbMATH DE number 1096053