The Stacks project

Lemma 36.6.8. Let $X$ be a scheme. Let $T \subset X$ be a closed subset which can locally be cut out by at most $c$ elements of the structure sheaf. Then $\mathcal{H}^ i_ Z(\mathcal{F}) = 0$ for $i > c$ and any quasi-coherent $\mathcal{O}_ X$-module $\mathcal{F}$.

Proof. This follows immediately from the local description of $R\mathcal{H}_ T(\mathcal{F})$ given in Lemma 36.6.7. $\square$

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