Lemma 27.21.3. Let $f : X \to Y$ be a morphism of schemes. Let $\mathcal{G}$ be a quasi-coherent $\mathcal{O}_ Y$-module. If $\mathcal{G}$ is locally projective on $Y$, then $f^*\mathcal{G}$ is locally projective on $X$.

Proof. See Algebra, Lemma 10.93.1. $\square$

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