Lemma 64.6.2 (03T5)—The Stacks project

Processing math: 100%

Table of contents
Part 3: Topics in Scheme Theory
Chapter 64: The Trace Formula
Section 64.6: Derived categories
Lemma 64.6.2 (cite)

numberstags

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 August 14, 2016 at 13:40

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

Comment #2197 by Johan on August 29, 2016 at 15:16

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

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).

Comments (2)

Post a comment