Lemma 29.35.8 (02GC)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 29: Morphisms of Schemes
Section 29.35: Unramified morphisms
Lemma 29.35.8 (cite)

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Lemma 29.35.8. A closed immersion $i : Z \to X$ is unramified. It is G-unramified if and only if the associated quasi-coherent sheaf of ideals $\mathcal{I} = \mathop{\mathrm{Ker}}(\mathcal{O}_ X \to i_*\mathcal{O}_ Z)$ is of finite type (as an $\mathcal{O}_ X$ -module).

Proof. Follows from Lemma 29.21.7 and Algebra, Lemma 10.151.3. $\square$

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