Lemma 31.11.4 (0AXT)—The Stacks project

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Lemma 31.11.4. Let $X$ be an integral scheme. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$ -module. The torsion sections of $\mathcal{F}$ form a quasi-coherent $\mathcal{O}_ X$ -submodule $\mathcal{F}_{tors} \subset \mathcal{F}$ . The quotient module $\mathcal{F}/\mathcal{F}_{tors}$ is torsion free.

Proof. Omitted. See More on Algebra, Lemma 15.22.2 for the algebraic analogue. $\square$

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