Lemma 31.9.1. Let $f : T \to S$ be a morphism of schemes. Let $\mathcal{F}$ be a finite type quasi-coherent $\mathcal{O}_ S$-module. Then $f^{-1}\text{Fit}_ i(\mathcal{F}) \cdot \mathcal{O}_ T = \text{Fit}_ i(f^*\mathcal{F})$.

**Proof.**
Follows immediately from More on Algebra, Lemma 15.8.4 part (3).
$\square$

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