Lemma 64.12.2. Let $\Lambda $ be a left Noetherian ring and $K\in D(\Lambda )$. Then $K$ is perfect if and only if the two following conditions hold:

$K$ has finite $\text{Tor}$-dimension, and

for all $i \in \mathbf{Z}$, $H^ i(K)$ is a finite $\Lambda $-module.

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