Lemma 59.71.10 (0GKB)—The Stacks project

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Part 3: Topics in Scheme Theory
Chapter 59: Étale Cohomology
Section 59.71: Constructible sheaves
Lemma 59.71.10 (cite)

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Lemma 59.71.10. Let $\Lambda \to \Lambda '$ be a homomorphism of Noetherian rings. Let $X$ be a scheme. Let $\mathcal{F}$ be a constructible sheaf of $\Lambda$ -modules on $X_{\acute{e}tale}$ . Then $\mathcal{F} \otimes _{\underline{\Lambda }} \underline{\Lambda '}$ is a constructible sheaf of $\Lambda '$ -modules.

Proof. Omitted. Hint: affine locally you can use the same stratification. $\square$

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