Lemma 61.27.3 (09B5)—The Stacks project

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Part 3: Topics in Scheme Theory
Chapter 61: Pro-étale Cohomology
Section 61.27: Constructible sheaves on the pro-étale site
Lemma 61.27.3 (cite)

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Lemma 61.27.3. Let $X$ be a scheme. Let $\Lambda$ be a Noetherian ring. The category of constructible sheaves of $\Lambda$ -modules on $X_{pro\text{-}\acute{e}tale}$ is a weak Serre subcategory of $\textit{Mod}(X_{pro\text{-}\acute{e}tale}, \Lambda )$ .

Proof. This is a formal consequence of Lemmas 61.27.2 and 61.19.8 and the result for the étale site (Étale Cohomology, Lemma 59.71.6). $\square$

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