EVENT DETAILS AND ABSTRACT

Title: The intersection homology D-module in finite characteristic
Speaker: Professor Manuel Blickle
Speaker Info: Essen
Brief Description:
Special Note:
Abstract:

Let Y be a normal subvariety of codimension c in the smooth k-variety X. If k is the field complex numbers it was shown by Kashiwara and Brylinski, using the theory of holonomic D modules, that the local cohomology module H^c_{[Y]}(X) contains a unique simple D submodule L (D being the sheaf of rings of differential operators on X). Under the Riemman-Hilbert correspondence, L corresponds to the Goreski-MacPhersons intersection homology complex. In my talk I will show how the existence of a unique simple D-submodule of H^c_{[Y]}(X) can be proved if k is a field of positive characteristic. The techniques used in characteristic zero are of no use, essentially due to the lack of a theory of holonomic D-modules in finite characteristic. Instead I use the theory of tight closure and O_X[F]-modules. The proof is constructive enough to give a fairly concrete D simplicity criterion for H^c_{[Y]}(X).