The Stacks project

Lemma 15.74.7. Let $R$ be a ring. If $K^\bullet \in D^ b(R)$ and all its cohomology modules are perfect, then $K^\bullet $ is perfect.

Proof. Follows by induction on the length of the finite complex: use Lemma 15.74.4 and the canonical truncations. $\square$

Comments (2)

Comment #95 by Sergei on

Why is not the complex (so with trivial differential) not a counterexample to Lemma 45.7 (in More Algebra) ?

Comment #96 by Johan on

Fixed. Thanks!

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  • 7 comment(s) on Section 15.74: Perfect complexes

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