The Stacks project

Definition 34.3.15. In the situation of Lemma 34.3.14 the functor $i_ S^{-1} = \pi _{S, *}$ is often called the restriction to the small Zariski site, and for a sheaf $\mathcal{F}$ on the big Zariski site we denote $\mathcal{F}|_{S_{Zar}}$ this restriction.