Search: This Site | People | Departments | Penn State
Topology/Geometry Seminar
Thursday, October 23, 2008
5:00 pm,
210 LRC
Jim Gillespie
Penn State University
Gorenstein model structures and generalized derived categories.
Abstract: This talk is based on recent joint work with Mark Hovey. First, we will give an alternate way to construct the derived category of a ring. The method is to use the fact that Z[x]/(x^2) is a graded Gorenstein ring and so the category of graded modules over this ring has the "Gorenstein projective model structure". But we will explain how this model category is exactly the category of unbounded chain complexes of abelian groups with the usual projective model structure. Now given any ring R, a theorem of Kan allows us to lift this model structure to the category of chain complexes of R-modules. Its homotopy category is the usual derived category D(R). But this construction works if we replace Z[x]/(x^2) by any other graded Gorenstein ring A (which is also flat as a Z-module). From this perspective we may think of D(R) as the derived category with respect to Z[x]/(x^2) and define more general derived categories D_A(R). We expect these to be Morita invariants and are looking for examples of rings R and S for which D(R) is equivalent to D(S), but D_A(R) is not equivalent to D_A(S) for some flat graded Gorenstein ring A.
We meet weekly on Thursday afternoons, alternating between Penn State Altoona and Penn State University Park. If you are interested in giving a talk in our seminar please contact one of the coordinators for the Fall 2008 semester: Wojtek Dorabiala and Aissa Wade.
