In the last chapter we introduced a notion of support for triangulated categories. The starting point in this one is a notion that we call ‘stratification’ for an Rlinear triangulated category T. It identifies conditions under which support can be used to parameterise localising subcategories of T. The crux of the stratification condition is local in nature, in that it involves only the subcategories GpT, so can be, and usually is, verified one prime at a time. We illustrate this technique by outlining the proof of the main results of this seminar; all this is part of Section 4.1. At first glance, the stratification condition is rather technical and of limited scope. To counter this, in Section 4.2 we discuss a number of interesting consequences that follow from this property. The last section has a different flavour: it makes concrete some of the ideas and constructions we have been discussing by describing them in the case of the Klein four group.
KeywordsGroup Algebra Compact Object Triangulate Category Tensor Ideal Commutative Noetherian Ring
Unable to display preview. Download preview PDF.