The intersection homology D-module in finite characteristic

2002/10/31 by Manuel Blickle
Mathematics · #math.AG #math.AC #msc:14B15 #msc:13N10

paper · pdf

published as Math. Ann. 328, 425-450 (2004) · 23 pages, streamlined exposition according to referee's suggestions

arxiv created 2004/03/01 · arxiv updated 2009/11/30

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).

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