Lemma 57.51.6. Let $f: X\to Y$ be a morphism of schemes and $\mathcal{F}\in \textit{Ab}(X_{\acute{e}tale})$. Then $R^ pf_*\mathcal{F}$ is the sheaf associated to the presheaf

$(V \to Y) \longmapsto H_{\acute{e}tale}^ p(X \times _ Y V, \mathcal{F}|_{X \times _ Y V}).$

Proof. This lemma is valid for topological spaces, and the proof in this case is the same. See Cohomology on Sites, Lemma 21.7.4 for details. $\square$

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).