The Stacks project

Lemma 61.11.2. Let $f : X \to Y$ be a separated quasi-finite morphism of quasi-compact and quasi-separated schemes. Let $\Lambda $ be a torsion coefficient ring. The functor $Rf^! : D(Y_{\acute{e}tale}, \Lambda ) \to D(X_{\acute{e}tale}, \Lambda )$ of Lemma 61.11.1 is the same as the functor $Rf^!$ of Lemma 61.7.1.

Proof. Follows from uniqueness of adjoints as $Rf_! = f_!$ by Lemma 61.10.3. $\square$


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