Lemma 31.12.6. Let $f : X \to Y$ be a flat morphism of integral locally Noetherian schemes. Let $\mathcal{G}$ be a coherent reflexive $\mathcal{O}_ Y$-module. Then $f^*\mathcal{G}$ is a coherent reflexive $\mathcal{O}_ X$-module.

**Proof.**
Omitted. See More on Algebra, Lemma 15.22.4 for the algebraic analogue.
$\square$

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