Lemma 31.11.8. Let X be an integral scheme. Let \mathcal{F} be a quasi-coherent \mathcal{O}_ X-module. Then \mathcal{F} is torsion free if and only if \mathcal{F}_ x is a torsion free \mathcal{O}_{X, x}-module for all x \in X.
Proof. Omitted. See More on Algebra, Lemma 15.22.6. \square
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