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The Stacks project

Lemma 63.11.2. 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 63.11.1 is the same as the functor Rf^! of Lemma 63.7.1.

Proof. Follows from uniqueness of adjoints as Rf_! = f_! by Lemma 63.10.3. \square

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