Lemma 31.11.3 (0AXS)—The Stacks project

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Lemma 31.11.3. Let $X$ be an integral scheme. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$ -module. The following are equivalent

$\mathcal{F}$ is torsion free,
for $U \subset X$ affine open $\mathcal{F}(U)$ is a torsion free $\mathcal{O}(U)$ -module.

Proof. Omitted. $\square$

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