Lemma 61.19.2. Let $X$ be a scheme. For every sheaf $\mathcal{F}$ on $X_{\acute{e}tale}$ the adjunction map $\mathcal{F} \to \epsilon _*\epsilon ^{-1}\mathcal{F}$ is an isomorphism, i.e., $\epsilon ^{-1}\mathcal{F}(U) = \mathcal{F}(U)$ for $U$ in $X_{\acute{e}tale}$.

Proof. Follows immediately from the description of $\epsilon ^{-1}$ in Lemma 61.19.1. $\square$

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