Definition 34.6.6. A *big syntomic site* is any site $\mathit{Sch}_{syntomic}$ as in Sites, Definition 7.6.2 constructed as follows:

Choose any set of schemes $S_0$, and any set of syntomic coverings $\text{Cov}_0$ among these schemes.

As underlying category take any category $\mathit{Sch}_\alpha $ constructed as in Sets, Lemma 3.9.2 starting with the set $S_0$.

Choose any set of coverings as in Sets, Lemma 3.11.1 starting with the category $\mathit{Sch}_\alpha $ and the class of syntomic coverings, and the set $\text{Cov}_0$ chosen above.

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