K-theory for triangulated categories, by Grigory Garkusha

[The preprint has been withdrawn by the author, and the files have been deleted.]

To any small triangulated category a K-theory K(T) is associated. We introduce the class of W-triangulated categories and prove the appriximation, additivity and localization theorems for them. The most important for applications examples of W-triangulated categories are derived categories and the stable category of a locally finite group. We also show that Quillen's K-theory of an exact category E is homotopy equivalent to the K-theory for the bounded derived category of E.

Important addendum from the author, March 16, 2002:

Marco Schlichting has constructed counter-examples (the preprint is available at his homepage) which contradict author's preprint 'K-theory for triangulated categories'. Thus main results of my preprint are wrong.

P.S. I should like to thank Paul Balmer who has given me the reference to Schlichting's preprint.

Grigory Garkusha <ggarkusha@mail.ru>