The Stacks project

Definition 34.6.8. Let $S$ be a scheme. Let $\mathit{Sch}_{syntomic}$ be a big syntomic site containing $S$.

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

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