The Stacks project

Lemma 63.11.1. Let $f : X \to Y$ be a finite type separated morphism of quasi-compact and quasi-separated schemes. Let $\Lambda $ be a torsion coefficient ring. The functor $Rf_! : D(X_{\acute{e}tale}, \Lambda ) \to D(Y_{\acute{e}tale}, \Lambda )$ has a right adjoint $Rf^! : D(Y_{\acute{e}tale}, \Lambda ) \to D(X_{\acute{e}tale}, \Lambda )$.

Proof. This follows from Injectives, Proposition 19.15.2 and Lemma 63.10.1 above. $\square$

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