K-theory for triangulated categories 3 3/4

Abstract

Let script T be a triangulated category, and assume it admits at least one model. In this article, we define a K-theory for script T. The main theorem is that, given any bounded t-structure on script T, the K-theory of the heart agrees with the K-theory of script T. An immediate consequence tells us that, if two Abelian categories occur as hearts of a triangulated category for two different t-structures, then their K-theories must be isomorphic. The proof was also sketched in previous articles in this series. The virtue of this article is in the careful detail in which it is written down. Show more