The Stacks project

Lemma 25.6.5. Let $\mathcal{C}$ be a site with equalizers and fibre products. Let $K$ be a hypercovering. Let $\mathcal{F}$ be an abelian sheaf. There is a spectral sequence $(E_ r, d_ r)_{r \geq 0}$ with

\[ E_2^{p, q} = \check{H}^ p(K, \underline{H}^ q(\mathcal{F})) \]

converging to the global cohomology groups $H^{p + q}(\mathcal{F})$.

Proof. This is a special case of Lemma 25.6.4. $\square$

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