Lemma 84.36.6. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $U$ be a simplicial algebraic space over $S$. Let $a : U \to X$ be an augmentation. Let $\mathcal{F}$ be an abelian sheaf on $X_{\acute{e}tale}$. Let $\mathcal{F}_ n$ be the pullback to $U_{n, {\acute{e}tale}}$. If $U$ is a ph hypercovering of $X$, then there exists a canonical spectral sequence

converging to $H^{p + q}_{\acute{e}tale}(X, \mathcal{F})$.

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