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Quot Functors for Deligne-Mumford Stacks

Martin Olsson·Jason Starr
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Abstract

Given a separated and locally finitely-presented Deligne-Mumford stack $\cX$ over an algebraic space $S$, and a locally finitely-presented $\OO_{\cX}$-module $\cF$, we prove that the Quot functor $\text{Quot}(\cF/\cX/S)$ is represented by a separated and locally finitely-presented algebraic space over $S$. Under additional hypotheses, we prove that the connected components of $\text{Quot}(\cF/\cX/S)$ are quasi-projective over $S$.

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Martin Olsson, Jason Starr. 2008-09-18. Quot Functors for Deligne-Mumford Stacks. https://arxiv.org/abs/math/0204307

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