Lemma 34.6.2. 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, see Morphisms, Lemma 29.34.7 and Lemma 34.5.2.
$\square$

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