The Stacks project

Definition 66.19.6. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $\mathcal{F}$ be a presheaf on $X_{\acute{e}tale}$. Let $\overline{x}$ be a geometric point of $X$. The stalk of $\mathcal{F}$ at $\overline{x}$ is

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

where $(U, \overline{u})$ runs over all étale neighborhoods of $\overline{x}$ in $X$ with $U \in \mathop{\mathrm{Ob}}\nolimits (X_{\acute{e}tale})$.

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