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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