The Stacks project

Lemma 71.5.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Let $\mathcal{F}$ be a finite type, quasi-coherent $\mathcal{O}_ Y$-module. Then $f^{-1}\text{Fit}_ i(\mathcal{F}) \cdot \mathcal{O}_ X = \text{Fit}_ i(f^*\mathcal{F})$.

Proof. Reduces to Divisors, Lemma 31.9.1 by étale localization. $\square$

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