Summary: RELATIVE ARTIN MOTIVES AND THE REDUCTIVE
BOREL-SERRE COMPACTIFICATION OF A LOCALLY
JOSEPH AYOUB AND STEVEN ZUCKER
Abstract. We introduce the notion of Artin motives and cohomological motives
over a scheme X. Given a cohomological motive M over X, we construct its
punctual weight zero part 0
X(M) as the universal Artin motive mapping to M.
We use this to define a motive EX 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 0
the computation of the motives EX.
In the second half of the paper, we develop the application to locally symmetric
varieties. More specifically, let \D be a locally symmetric variety and denote by
p : \D
the projection of its reductive Borel-Serre compactification
to its Baily-Borel Satake compactification. We show that RpQ\D