Proposition 99.10.2 (0D04)—The Stacks project

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Table of contents
Part 7: Algebraic Stacks
Chapter 99: Quot and Hilbert Spaces
Section 99.10: The Picard stack
Proposition 99.10.2 (cite)

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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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