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Definition 34.5.8. Let $S$ be a scheme. Let $\mathit{Sch}_{smooth}$ be a big smooth site containing $S$.

  1. The big smooth site of $S$, denoted $(\mathit{Sch}/S)_{smooth}$, is the site $\mathit{Sch}_{smooth}/S$ introduced in Sites, Section 7.25.

  2. The big affine smooth site of $S$, denoted $(\textit{Aff}/S)_{smooth}$, is the full subcategory of $(\mathit{Sch}/S)_{smooth}$ whose objects are affine $U/S$. A covering of $(\textit{Aff}/S)_{smooth}$ is any covering $\{ U_ i \to U\} $ of $(\mathit{Sch}/S)_{smooth}$ which is a standard smooth covering.

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