The Stacks project

Lemma 48.9.2. With notation as above. The functor $R\mathop{\mathcal{H}\! \mathit{om}}\nolimits (\mathcal{O}_ Z, -)$ is the right adjoint of the functor $Ri_* : D(\mathcal{O}_ Z) \to D(\mathcal{O}_ X)$.

Proof. This is a consequence of the fact that $i_*$ and $\mathop{\mathcal{H}\! \mathit{om}}\nolimits (\mathcal{O}_ Z, -)$ are adjoint functors by Lemma 48.9.1. See Derived Categories, Lemma 13.30.3. $\square$

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