Lemma 73.7.2 (0DFC)—The Stacks project

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Part 4: Algebraic Spaces
Chapter 73: Topologies on Algebraic Spaces
Section 73.7: Fppf topology
Lemma 73.7.2 (cite)

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Lemma 73.7.2. Any syntomic covering is an fppf covering, and a fortiori, any smooth, étale, or Zariski covering is an fppf covering.

Proof. This is clear from the definitions, the fact that a syntomic morphism is flat and locally of finite presentation (Morphisms of Spaces, Lemmas 67.36.5 and 67.36.6) and Lemma 73.6.2. $\square$

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