Lemma 108.8.1 (0DMA)—The Stacks project

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Table of contents
Part 8: Topics in Moduli Theory
Chapter 108: Moduli Stacks
Section 108.8: Properties of the Picard stack
Lemma 108.8.1 (cite)

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Lemma 108.8.1. The diagonal of $\mathcal{P}\! \mathit{ic}_{X/B}$ over $B$ is affine and 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 108.4.1. $\square$

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