### Relative Artin motives and the reductive Borel-Serre compactification of a locally symmetric variety, by Joseph Ayoub and Steven Zucker

We introduce the notion of Artin motives and cohomological motives over a
scheme X. Given a cohomological motive M over X, we construct its weight-zero
part as the universal Artin motive mapping to M. We use this to define a
motive E_X over X which is an invariant of the singularities of X. We then
give an application to locally symmetric varieties. Namely, we prove that the
Betti realization of E_X for X the Baily-Borel compactification is isomorphic
to the cohomological direct image of the constant sheaf Q along the projection
from the reductive Borel-Serre compactification to the Baily-Borel
compactification.

Joseph Ayoub <joseph.ayoub@math.uzh.ch>

Steven Zucker <zucker@jhu.edu>