Lemma 61.12.22 (098Z)—The Stacks project

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Table of contents
Part 3: Topics in Scheme Theory
Chapter 61: Pro-étale Cohomology
Section 61.12: The pro-étale site
Lemma 61.12.22 (cite)

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Lemma 61.12.22. Let $S$ be a scheme. The topology on each of the pro-étale sites $\mathit{Sch}_{pro\text{-}\acute{e}tale}$ , $S_{pro\text{-}\acute{e}tale}$ , $(\mathit{Sch}/S)_{pro\text{-}\acute{e}tale}$ , $S_{affine, {pro\text{-}\acute{e}tale}}$ , and $(\textit{Aff}/S)_{pro\text{-}\acute{e}tale}$ is subcanonical.

Proof. Combine Lemma 61.12.2 and Descent, Lemma 35.13.7. $\square$

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