Lemma 47.15.9. Let $A \to B$ be a surjective homomorphism of Noetherian rings. Let $\omega _ A^\bullet $ be a dualizing complex. Then $R\mathop{\mathrm{Hom}}\nolimits (B, \omega _ A^\bullet )$ is a dualizing complex for $B$.

**Proof.**
Special case of Lemma 47.15.8.
$\square$

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