The Stacks project

Lemma 38.34.6. An fppf covering is a h covering. Hence syntomic, smooth, étale, and Zariski coverings are h coverings as well.

Proof. This is true because in an fppf covering the morphisms are required to be locally of finite presentation and because fppf coverings are ph covering, see More on Morphisms, Lemma 37.48.7. The second statement follows from the first and Topologies, Lemma 34.7.2. $\square$

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