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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