The Stacks project

Lemma 31.12.3. Let $f : X \to Y$ be a dominant morphism of integral schemes. Let $\mathcal{G}$ be a quasi-coherent $\mathcal{O}_ Y$-module. Then the rank of $\mathcal{G}$ on $Y$ is equal to the rank of $f^*\mathcal{G}$ on $X$.

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