Definition 92.12.2. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$. Let $\mathcal{X}$ be an algebraic stack over $S$. We say $\mathcal{X}$ is a Deligne-Mumford stack if there exists a scheme $U$ and a surjective étale morphism $(\mathit{Sch}/U)_{fppf} \to \mathcal{X}$.

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