The Stacks project

Lemma 34.10.10. Any fpqc covering is a V covering. A fortiori, any fppf, syntomic, smooth, ├ętale or Zariski covering is a V covering. Also, a ph covering is a V covering.

Proof. An fpqc covering can affine locally be refined by a standard fpqc covering, see Lemmas 34.9.9. A standard fpqc covering is a standard V covering, see Lemma 34.10.2. Hence the first statement follows from our definition of V covers in terms of standard V coverings. The conclusion for fppf, syntomic, smooth, ├ętale or Zariski coverings follows as these are fpqc coverings, see Lemma 34.9.7.

The statement on ph coverings follows from Lemma 34.10.3 in the same manner. $\square$

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