Motives of Deligne-Mumford Stacks, by Utsav Choudhury

For every smooth and separated Deligne-Mumford stack F, we associate a motive M(F) in Voevodsky's category of mixed motives with rational coefficients. When F is proper over a field of characteristic 0, we compare M(F) with the Chow motive associated to F by Toen. Without the properness condition we show that M(F) is a direct summand of the motive of a smooth quasi-projective variety.

Utsav Choudhury <>