Lemma 65.26.2. Let $S$ be a scheme. Let

be a cartesian square of algebraic spaces over $S$. Let $\mathcal{F} \in \textit{Mod}(\mathcal{O}_ X)$. If $g$ is étale, then $f'_*(\mathcal{F}|_{X'}) = (f_*\mathcal{F})|_{Y'}$^{1} and $R^ if'_*(\mathcal{F}|_{X'}) = (R^ if_*\mathcal{F})|_{Y'}$ in $\textit{Mod}(\mathcal{O}_{Y'})$.

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