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}).
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