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Oct 4, 2017 at 17:30 comment added Mikhail Bondarko However, do you want to consider certain rational homotopy types of these bounded derived categories? Then you should specify some model category containing them as objects.
Sep 28, 2017 at 17:02 comment added Mikhail Bondarko And if the characteristic of the field is positive then this operation kills everything.:)
Sep 27, 2017 at 23:11 vote accept user114292
Sep 27, 2017 at 22:02 comment added Sasha @user114292 If everything is over a field of zero characteristic this cone is already zero, so your operation changes nothing.
Sep 27, 2017 at 22:00 comment added user114292 By this, I mean you take the triangulated category, and you do Verdier quotient so that $Cone(E\xrightarrow{n\cdot id_E} E)\simeq 0$ for every object $E$ and every nonzero integer $n$.
Sep 27, 2017 at 21:49 comment added Sasha @user114292 In what sense do you rationalize?
Sep 27, 2017 at 21:46 comment added user114292 Even the rational bounded derived categories are different? By rational, I mean you rationalize the triangulated category.
Sep 27, 2017 at 18:28 history answered Sasha CC BY-SA 3.0