2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/169327Given 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 $S$.20 pages. A Mistake in Section 4 is corrected in this version and in the published versionAlgebraic Geometry14J10text