Motivic Weight Complexes for Arithmetic Varieties

Details Motivic Weight Complexes for Arithmetic Varieties Motivic Weight Complexes for Arithmetic Varieties

2008-04-30

arxiv.org/abs/0804.4853v2

Mathematics

Algebraic Geometry

52 pages. Proofs in section 56 have been clarified and a new section on Chow motives has been added

Scientific paper

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.

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