Suppose $\mathcal{F}$ is a sheaf on the big étale site of $S$. Let $T \to S$ be an object of the big étale site of $S$, and let $\overline{t}$ be a geometric point of $T$. Then we define $\mathcal{F}_{\overline{t}}$ as the stalk of the restriction $\mathcal{F}|_{T_{\acute{e}tale}}$ of $\mathcal{F}$ to the small étale site of $T$. In other words, we can define the stalk of $\mathcal{F}$ at any geometric point of any scheme $T/S \in \mathop{\mathrm{Ob}}\nolimits ((\mathit{Sch}/S)_{\acute{e}tale})$.
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