The Stacks project

Proposition 59.54.2 (Leray spectral sequence). Let $f: X \to Y$ be a morphism of schemes and $\mathcal{F}$ an étale sheaf on $X$. Then there is a spectral sequence

\[ E_2^{p, q} = H_{\acute{e}tale}^ p(Y, R^ qf_*\mathcal{F}) \Rightarrow H_{\acute{e}tale}^{p+q}(X, \mathcal{F}). \]

Proof. See Lemma 59.54.1 and see Derived Categories, Section 13.22. $\square$

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