On motives for Deligne-Mumford stacks

Details On motives for Deligne-Mumford stacks On motives for Deligne-Mumford stacks

2000-06-21

arxiv.org/abs/math/0006160v1

Mathematics

Algebraic Geometry

19 pages. To appear in IMRN

Scientific paper

We define and compare two different definitions of Chow motives for Deligne-Mumford stacks, associated with two definitions of Chow rings. The main result we prove is that both categories of motives are equivalent to the usual category of motives of algebraic varieties, but the motives of a given stack associated with both theories are not isomorphic. We will also give some examples of motives associated with some alegbraic stacks.

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