### Motivic Weight Complexes for Arithmetic Varieties, by Henri Gillet and Christophe Soulé

We associate weight complexes of (homological) motives, and hence
Euler characteristics in the Grothendieck group of motives, to
arithmetic varieties and Deligne-Mumford stacks; this extends the
results in the paper "Descent, Motives and K-theory" in volume 478 of
Crelle, where a similar result was proved for varieties over a field of
characteristic zero. We use K_0-motives with rational coefficients,
rather than Chow motives, because we cannot appeal to resolution of
singularities, but rather must use de Jong's results. In addition, for
varieties over a field we prove a general result on contravariance of
weight complexes, in particular showing that any morphism of finite
tor-dimension between varieties induces a morphism of weight complexes.

See http://arxiv.org/abs/0804.4853.

Henri Gillet <henri@math.uic.edu>

Christophe Soulé <soule@ihes.fr>