Algebraic Geometry Seminar

It is an important problem to define a K-theoretic version of intersection cohomology, with expected applications in representation theory. One step further is to look for a categorification of intersection cohomology. For good moduli spaces X of Artin stack Y (as defined by Alper), we construct some noncommutative resolutions D(X) inside the category D^b(Y). Further, we construct subcategories I(X) of D(X) whose periodic cyclic homology is given by the intersection cohomology of X. In particular, the K-theory of I(X) is a natural definition of intersection K-theory for the variety X. Speaker(s): Tudor Padurariu (IAS)