Definition 59.29.6. Let $S$ be a scheme. Let $\mathcal{F}$ be a presheaf on $S_{\acute{e}tale}$. Let $\overline{s}$ be a geometric point of $S$. The *stalk* of $\mathcal{F}$ at $\overline{s}$ is

\[ \mathcal{F}_{\overline{s}} = \mathop{\mathrm{colim}}\nolimits _{(U, \overline{u})} \mathcal{F}(U) \]

where $(U, \overline{u})$ runs over all étale neighborhoods of $\overline{s}$ in $S$.

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