Lemma 108.8.2 (0DMB)—The Stacks project

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Part 8: Topics in Moduli Theory
Chapter 108: Moduli Stacks
Section 108.8: Properties of the Picard stack
Lemma 108.8.2 (cite)

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Lemma 108.8.2. The morphism $\mathcal{P}\! \mathit{ic}_{X/B} \to B$ is quasi-separated and locally of finite presentation.

Proof. In Quot, Lemma 99.10.1 we have seen that $\mathcal{P}\! \mathit{ic}_{X/B}$ is an open substack of $\mathcal{C}\! \mathit{oh}_{X/B}$ . Hence this follows from Lemma 108.4.2. $\square$

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