Lemma 34.8.5 (0DBH)—The Stacks project

Table of contents
Part 2: Schemes
Chapter 34: Topologies on Schemes
Section 34.8: The ph topology
Lemma 34.8.5 (cite)

Lemma 34.8.5. A Zariski covering is a ph covering ¹.

Proof. This is true because a Zariski covering of an affine scheme can be refined by a standard ph covering by Lemma 34.8.3. $\square$

[1] We will see in More on Morphisms, Lemma 37.48.7 that fppf coverings (and hence syntomic, smooth, or étale coverings) are ph coverings as well.

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