The Stacks project

Lemma 30.2.6. Let $X$ be a scheme. Let $\mathcal{U} : X = \bigcup _{i \in I} U_ i$ be an open covering such that $U_{i_0 \ldots i_ p}$ is affine open for all $p \ge 0$ and all $i_0, \ldots , i_ p \in I$. In this case for any quasi-coherent sheaf $\mathcal{F}$ we have

\[ \check{H}^ p(\mathcal{U}, \mathcal{F}) = H^ p(X, \mathcal{F}) \]

as $\Gamma (X, \mathcal{O}_ X)$-modules for all $p$.

Proof. In view of Lemma 30.2.2 this is a special case of Cohomology, Lemma 20.11.6. $\square$

Comments (1)

Comment #931 by correction_bot on

Missing a period in the statement of the lemma.

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