Lemma 17.11.4 (01BQ)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 17: Sheaves of Modules
Section 17.11: Modules of finite presentation
Lemma 17.11.4 (cite)

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Lemma 17.11.4. Let $f : (X, \mathcal{O}_ X) \to (Y, \mathcal{O}_ Y)$ be a morphism of ringed spaces. The pullback $f^*\mathcal{G}$ of a module of finite presentation is of finite presentation.

Proof. Exactly the same as the proof of Lemma 17.10.4 but with finite index sets. $\square$

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