The Stacks project

Lemma 73.6.2. Any smooth covering is a syntomic covering, and a fortiori, any étale or Zariski covering is a syntomic covering.

Proof. This is clear from the definitions and the fact that a smooth morphism is syntomic (Morphisms of Spaces, Lemma 67.37.8), and Lemma 73.5.2. $\square$

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