The Stacks project

Lemma 71.5.2. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $\mathcal{F}$ be a finitely presented $\mathcal{O}_ X$-module. Then $\text{Fit}_ r(\mathcal{F})$ is a quasi-coherent ideal of finite type.

Proof. Reduces to Divisors, Lemma 31.9.2 by étale localization. $\square$

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