Lemma 15.73.7. 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 15.73.4 and the canonical truncations. $\square$
Post a comment
Your email address will not be published. Required fields are marked.
In your comment you can use Markdown and LaTeX style mathematics (enclose it like
$\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).
All contributions are licensed under the GNU Free Documentation License.