Algebraic Geometry Seminar

Manuel Blickle (Essen)

"The intersection homology D--module in finite characteristic"

Let Y be a normal subvaritey of a smooth k-variety X of codimension c. If k is the field of complex numbers, Brylinski and Kashiwara showed that the local cohomology module with sections supported in Y, (H^c_{[Y]}(X,O_X)) contains a unique simple D_X--submodule, denoted by L(Y,X). Under the Riemann--Hilbert correspondence L(Y,X) corresponds to Goreski-MacPherson's intersection homology complex. Im my talk I will prove the analog of the above result if k is a field of positive characteristic. The techniques used originate in the theory of tight closure and a theory of modules with a Frobenius action. The given proof is constructive enough to yield a fairly concrete D-simplicity criterion for H^c_{[Y]}(X,O_X).