The Stacks project

Proposition 99.10.2. Let $S$ be a scheme. Let $f : X \to B$ be a morphism of algebraic spaces over $S$. If $f$ is flat, of finite presentation, and proper, then $\mathcal{P}\! \mathit{ic}_{X/B}$ is an algebraic stack.

Proof. Immediate consequence of Lemma 99.10.1, Algebraic Stacks, Lemma 94.15.4 and either Theorem 99.5.12 or Theorem 99.6.1 $\square$

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