Lemma 17.14.3 (01C8)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 17: Sheaves of Modules
Section 17.14: Locally free sheaves
Lemma 17.14.3 (cite)

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Lemma 17.14.3. Let $f : (X, \mathcal{O}_ X) \to (Y, \mathcal{O}_ Y)$ be a morphism of ringed spaces. If $\mathcal{G}$ is a locally free $\mathcal{O}_ Y$ -module, then $f^*\mathcal{G}$ is a locally free $\mathcal{O}_ X$ -module.

Proof. Omitted. $\square$

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