Motives of Deligne-Mumford Stacks

2011/09/24 by Choudhury, Utsav
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1109.5288

Abstract

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 DM^\eff(k,ℚ). When F is proper over a field of characteristic 0, we compare M(F) with the Chow motive associated to F by Toen (\citet). Without the properness condition we show that M(F) is a direct summand of the motive of a smooth quasi-projective variety.

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