Quot Functors for Deligne-Mumford Stacks

Details Quot Functors for Deligne-Mumford Stacks Quot Functors for Deligne-Mumford Stacks

2002-04-24

arxiv.org/abs/math/0204307v2

Comm. Algebra 31 (2003), no. 8, 4069--4096

Mathematics

Algebraic Geometry

20 pages. A Mistake in Section 4 is corrected in this version and in the published version

Scientific paper

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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