Lemma 108.10.1 (0DPM)—The Stacks project

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Table of contents
Part 8: Topics in Moduli Theory
Chapter 108: Moduli Stacks
Section 108.10: Properties of relative morphisms
Lemma 108.10.1 (cite)

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Lemma 108.10.1. The diagonal of $\mathit{Mor}_ B(Y, X) \to B$ is a closed immersion of finite presentation.

Proof. There is an open immersion $\mathit{Mor}_ B(Y, X) \to \mathrm{Hilb}_{Y \times _ B X/B}$ , see Quot, Lemma 99.12.2. Thus the lemma follows from Lemma 108.7.1. $\square$

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