Lemma 48.28.3. Let $X \to S$ be a morphism of schemes which is flat and locally of finite presentation. Let $(K, \xi )$ be a relative dualizing complex. Then $\mathcal{O}_ X \to R\mathop{\mathcal{H}\! \mathit{om}}\nolimits _{\mathcal{O}_ X}(K, K)$ is an isomorphism.

**Proof.**
Looking affine locally this reduces using Lemma 48.28.2 to the algebraic case which is Dualizing Complexes, Lemma 47.27.5.
$\square$

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