The Stacks project

Definition 102.9.1. Let $\mathcal{X}$ be an algebraic stack. A presheaf of $\mathcal{O}_\mathcal {X}$-modules $\mathcal{F}$ is parasitic if we have $\mathcal{F}(x) = 0$ for any object $x$ of $\mathcal{X}$ which lies over a scheme $U$ such that the corresponding morphism $x : U \to \mathcal{X}$ is flat.

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