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 HcY(X,OX) contains a unique simple DX-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 DX-simplicity of HcY(X).
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