Multiplier Ideals and Modules on Toric Varieties

A simple formula computing the multiplier ideal of a monomial ideal on an arbitrary affine toric variety is given. Variants for the multiplier module and test ideals are also treated.Comment: 8 pages, to appear in Mathematische Zeitschrif

The D-Module structure of R[F]-modules

Let R be a regular ring essentially of finite type over a perfect field k. An R-module M is called a unit R[F]-module if it comes equipped with an isomorphism F*M-->M where F denotes the Frobenius map on Spec R, and F* is the associated pullback functor. It is well known that M then carries a natural D-module structure. In this paper we investigate the relation between the unit R[F]-structure and the induced D-structure on M. In particular, it is shown that, if k is algebraically closed and M is a simple finitely generated unit R[F]-module, then it is also simple as a D-module. An example showing the necessity of k being algebraically closed is also given.Comment: 25 pages. Some minor changes following referee's suggestion. To appear in Trans. AM

The intersection homology D-module in finite characteristic

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).Comment: 23 pages, streamlined exposition according to referee's suggestion