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Relative Artin motives and the reductive Borel–Serre compactification of a locally symmetric variety |
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| Authors: | Joseph Ayoub Steven Zucker |
| Institution: | 1. Institut f??r Mathematik, Universit?t Z??rich, Winterthurerstr. 190, 8057, Zurich, Switzerland 2. CNRS, LAGA Universit?? Paris 13, 99 avenue J.B. Cl??ment, 93430, Villetaneuse, France 3. Department of Mathematics, Johns Hopkins University, Baltimore, MD, 21218, USA |
| Abstract: | 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 w0X(M)\omega^{0}_{X}(M). We use this to define a motive \mathbbEX\mathbb{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 w0X\omega^{0}_{X} and the computation of the motives \mathbbEX\mathbb{E}_{X}. |
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