Liran Shaul : The finitistic dimension conjecture via DG-rings
The finitistic dimension of a ring A is defined to be the supremum of projective dimensions among all A-modules of finite projective dimension. It is an open problem whether this quantity is finite for finite dimensional algebras over a field and for artin algebras.
In this talk, I will explain a new approach for studying the finiteness of the finitistic dimension by embedding the ring A inside a nicely behaved differential graded algebra, and using relation between this DG-algebra and A to deduce results about the finitistic dimension. As an application of these methods, I will explain how to generalize a recent sufficient condition of Rickard, for FPD(A)<∞ in terms of generation of D(A) from finite dimensional algebras over a field to all left perfect rings which admit a dualizing complex.