The Stacks project

Lemma 64.6.2. An object $E$ of $D(\mathcal{A})$ is contained in $D^+(\mathcal{A})$ if and only if $H^ i(E) =0 $ for all $i \ll 0$. Similar statements hold for $D^-$ and $D^ b$.

Proof. Hint: use truncation functors. See Derived Categories, Lemma 13.11.5. $\square$

Comments (2)

Comment #2168 by Alex on

I think this was probably meant to link to Lemma 13.11.5 05RV rather than 13.11.6

Comment #2197 by on

OK, you are right. But of course the discussion in this section is lacking and one has to read a lot more about triangulated categories to correctly parse these statements... Fixed here.

There are also:

  • 6 comment(s) on Section 64.6: Derived categories

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Your email address will not be published.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).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 03T5. Beware of the difference between the letter 'O' and the digit '0'.