Definition 47.15.1. Let $A$ be a Noetherian ring. A *dualizing complex* is a complex of $A$-modules $\omega _ A^\bullet $ such that

$\omega _ A^\bullet $ has finite injective dimension,

$H^ i(\omega _ A^\bullet )$ is a finite $A$-module for all $i$, and

$A \to R\mathop{\mathrm{Hom}}\nolimits _ A(\omega _ A^\bullet , \omega _ A^\bullet )$ is a quasi-isomorphism.

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