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arXiv · 1109.5288

Motives of Deligne-Mumford Stacks

Utsav Choudhury
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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 $\mathbf{DM}^{\eff}(k,\mathbb{Q})$. When $F$ is proper over a field of characteristic 0, we compare $M(F)$ with the Chow motive associated to $F$ by Toen (\cite{t}). 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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Utsav Choudhury. 2012-08-30. Motives of Deligne-Mumford Stacks. https://arxiv.org/abs/1109.5288

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