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 $p$.
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Comment #931 by correction_bot on