The intersection homology D-module in finite characteristic

Abstract

For Y a closed normal subvariety of codimension c of a smooth complex variety X, Brylinski and Kashiwara showed that the local cohomology module H^c_Y(X,O_X) contains a unique simple D_X-submodule, denoted by L(Y,X). In this paper the analogous result is shown for X and Y defined over a perfect field of finite characteristic. Moreover, a local construction of Ll(Y,X) is given, relating it to the theory of tight closure. From the construction one obtains a criterion for the D_X-simplicity of H^c_Y(X).