Lemma 48.11.3 (0BV1)—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 48.11.3 (cite)

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Lemma 48.11.3. With notation as above. The composition

$D(\mathcal{O}_ X) \xrightarrow {R\mathop{\mathcal{H}\! \mathit{om}}\nolimits (f_*\mathcal{O}_ Y, -)} D(f_*\mathcal{O}_ Y) \to D(\mathcal{O}_ X)$

is the functor $K \mapsto R\mathop{\mathcal{H}\! \mathit{om}}\nolimits _{\mathcal{O}_ X}(f_*\mathcal{O}_ Y, K)$ .

Proof. This is immediate from the construction. $\square$

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