The Stacks project

Definition 59.27.3. (For more details see Section 59.20, or Topologies, Section 34.4.) Let $S$ be a scheme. The big étale site over $S$ is the site $(\mathit{Sch}/S)_{\acute{e}tale}$, see Definition 59.20.2. The small étale site over $S$ is the site $S_{\acute{e}tale}$, see Definition 59.20.2. We define similarly the big and small Zariski sites on $S$, denoted $(\mathit{Sch}/S)_{Zar}$ and $S_{Zar}$.

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