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.
Proof. See More on Algebra, Lemma 15.74.2 for the proof in the commutative case. \square
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