The Stacks project

Lemma 85.21.3. Let $\mathcal{C}$ be a site with fibre products and $X \in \mathop{\mathrm{Ob}}\nolimits (\mathcal{C})$. Let $a : U \to X$ be a hypercovering of $X$ in $\mathcal{C}$ as defined above. Then we have a canonical isomorphism

\[ R\Gamma (X, E) = R\Gamma ((\mathcal{C}/U)_{total}, a^{-1}E) \]

for $E \in D(\mathcal{C}/X)$.

Proof. This is a special case of Lemma 85.19.3. $\square$

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