The Stacks project

Lemma 31.9.2. Let $S$ be a scheme. Let $\mathcal{F}$ be a finitely presented $\mathcal{O}_ S$-module. Then $\text{Fit}_ r(\mathcal{F})$ is a quasi-coherent ideal of finite type.

Proof. Follows immediately from More on Algebra, Lemma 15.8.4 part (4). $\square$

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