The Stacks project

Lemma 59.77.6. Let $\Lambda $ be a Noetherian ring. Let $f : X \to Y$ be a morphism of schemes. If $K \in D_{ctf}(Y_{\acute{e}tale}, \Lambda )$ then $Lf^*K \in D_{ctf}(X_{\acute{e}tale}, \Lambda )$.

Proof. Apply Lemma 59.77.3 to reduce this to a question about finite complexes of flat constructible sheaves of $\Lambda $-modules. Then the statement follows as $f^{-1} = f^*$ is exact and Lemma 59.71.5. $\square$

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