Abstract
For Y a closed normal subvariety of codimension c of a smooth ℂ–variety X, Brylinski and Kashiwara showed that the local cohomology module ℋc Y (X, X ) contains a unique simple X –submodule, denoted by (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 (Y, X) is given, relating it to the theory of tight closure. From the construction one obtains a criterion for the X –simplicity of ℋc Y (X, X ).
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