Lemma 34.6.7. Let \mathit{Sch}_{syntomic} be a big syntomic site as in Definition 34.6.6. Let T \in \mathop{\mathrm{Ob}}\nolimits (\mathit{Sch}_{syntomic}). Let \{ T_ i \to T\} _{i \in I} be an arbitrary syntomic covering of T.
There exists a covering \{ U_ j \to T\} _{j \in J} of T in the site \mathit{Sch}_{syntomic} which refines \{ T_ i \to T\} _{i \in I}.
If \{ T_ i \to T\} _{i \in I} is a standard syntomic covering, then it is tautologically equivalent to a covering in \mathit{Sch}_{syntomic}.
If \{ T_ i \to T\} _{i \in I} is a Zariski covering, then it is tautologically equivalent to a covering in \mathit{Sch}_{syntomic}.
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