The Stacks project

Definition 31.11.2. Let $X$ be an integral scheme. Let $\mathcal{F}$ be a quasi-coherent $\mathcal{O}_ X$-module.

  1. We say a local section of $\mathcal{F}$ is torsion if it satisfies the equivalent conditions of Lemma 31.11.1.

  2. We say $\mathcal{F}$ is torsion free if every torsion section of $\mathcal{F}$ is $0$.

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View Definition 31.11.2 as pdf