The Stacks project

Lemma 96.26.2. In the situation of Definition 96.26.1 suppose that $M$ is an object of $\mathit{QC}(\mathcal{X})$ and $b \in \mathbf{Z}$ such that $H^ i(M) = 0$ for all $i > b$. Then $H^ b(M)$ is a quasi-coherent module on $(\mathcal{X}_{affine}, \mathcal{O})$, see Lemma 96.25.1.

Proof. Special case of Cohomology on Sites, Lemma 21.43.3. $\square$

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