## Algebra Topology Seminar: Nullity classes and t-structures in the derived category of a ring

- Date: 11/04/2009

University of British Columbia

In stable homotopy theory the thick subcategory theorem of Hopkins and Smith classifies thick subcategories of the triangulated category of p-torsion finite spectra. Unstably Bousfield classified nullity classes of p-torsion finite suspensions. We look at analagous results in the derived category of a commutative noetherian ring D(R), and some of its subcategories satisfying suitable finiteness conditions. Hopkins and later Neeman proved that thick subcategories of D_{perf}(R) can be classified by their supports, which are subsets of Spec(R). In analogy to Bousfield's result, we show that nullity classes in D^b_{fg}(R) can be classified by certain increasing functions from Z into Spec(R). By an observation of Keller and Vossieck, it turns out that t-structures are just nullity classes together with a right adjoint of the inclusion. From this we derive an extra condition that the increasing function must satisfy to correspond to a t-structure. When R has a dualizing complex, applying a construction of Deligne and Bezrukavnikov thengives a classification of all the t-sctructures in D^b_{fg}(R).

3:00pm - 4:00pm, WMAX 110.