Definition 34.7.8. Let $S$ be a scheme. Let $\mathit{Sch}_{fppf}$ be a big fppf site containing $S$.

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

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

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