## EVENT DETAILS AND ABSTRACT

**Algebra Seminar**
**Title:** The intersection homology D-module in finite characteristic

**Speaker:** Professor Manuel Blickle

**Speaker Info:** Essen

**Brief Description:**

**Special Note**:

**Abstract:**

Let Y be a normal subvariety of codimension c in the smooth
k-variety X. If k is the field complex numbers it was shown
by Kashiwara and Brylinski, using the theory of holonomic D modules,
that the local cohomology module H^c_{[Y]}(X) contains a unique simple
D submodule L (D being the sheaf of rings of differential
operators on X). Under the Riemman-Hilbert correspondence, L
corresponds to the Goreski-MacPhersons intersection homology complex.
In my talk I will show how the existence of a unique simple
D-submodule of H^c_{[Y]}(X) can be proved if k is a field of positive
characteristic. The techniques used in characteristic zero are of no
use, essentially due to the lack of a theory of holonomic D-modules in
finite characteristic. Instead I use the theory of tight closure and
O_X[F]-modules. The proof is constructive enough to give a
fairly concrete D simplicity criterion for H^c_{[Y]}(X).

**Date:** Tuesday, February 19, 2002

**Time:** 2:00 pm

**Where:** Lunt 101

**Contact Person:** Prof. Matthew Emerton

**Contact email:** emerton@math.northwestern.edu

**Contact Phone:** 847-491-5544

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