Triangulated defect categories

We will define certain Verdier quotients of the singularity category of a ring R, called defect categories. The triviality of these defect

categories determine, for example, whether a commutative local ring is Gorenstein, or a complete intersection. The dimension (in the sense of Rouquier) of the defect category thus gives a measure of how close such a ring is to being Gorenstein, respectively, a complete intersection. Examples will be given. This is based on joint work with Petter Bergh and Steffen Oppermann.