Lemma 48.11.2 (0BV0)—The Stacks project

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Part 3: Topics in Scheme Theory
Chapter 48: Duality for Schemes
Section 48.11: Right adjoint of pushforward for finite morphisms
Lemma 48.11.2 (cite)

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Lemma 48.11.2. With notation as above. The functor $R\mathop{\mathcal{H}\! \mathit{om}}\nolimits (f_*\mathcal{O}_ Y, -)$ is the right adjoint of the functor $D(f_*\mathcal{O}_ Y) \to D(\mathcal{O}_ X)$ .

Proof. Follows from Lemma 48.11.1 and Derived Categories, Lemma 13.30.3. $\square$

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