Relative Artin motives and the reductive Borel-Serre compactification of a locally symmetric variety

• 成果类型: Article
• 署名作者: Ayoub, Joseph; Zucker, Steven
• 署名单位: University of Zurich; Universite Paris 13; Centre National de la Recherche Scientifique (CNRS); Johns Hopkins University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-011-0349-0
• 发表日期: 2012
• 页码: 277-427
• 关键词: algebraic variety; SINGULARITIES; COHOMOLOGY; RESOLUTION; quotients; field

摘要

We introduce the notion of Artin motives and cohomological motives over a scheme X. Given a cohomological motive M over X, we consider the universal Artin motive mapping to M and denote it omega(0)(X) ( M). We use this to define a motive E-X over X which is an invariant of the singularities of X. The first half of the paper is devoted to the study of the functors omega(0)(X) and the computation of the motives E-X.