# AGANT SEMINAR

### (Algebraic Geometry, Algebra and Number Theory Seminar)

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__Date/Time/Room:__ Thursday, May 2, 2002, at 5:00 pm in 487 Pickard Hall

__Speaker:__
David Jorgensen,
Department of Mathematics,
UTA

*``Building Modules Having a Prescribed
Cohomological Support Set''*

**Abstract:**
Suppose R is a graded complete intersection, that is, a quotient of a
polynomial ring k[x_{1},...,x_{n}] by a regular sequence of
homogeneous polynomials f_{1},...,f_{c}. Given a finitely
generated graded R-module M, it turns out that the sequence of Ext modules
E:=Ext^{*}_{R}(M,k) has the structure of graded module over
a polynomial ring S:=k[z_{1},...,z_{c}]. The cone in
k^{c} defined by ann_{S}(E) is called the cohomological
support set of M. These cohomological support sets offer a useful means of
classifying finitely generated R-modules. In this talk, we will give some
background on cohmological support sets and then discuss an algorithm
written by myself and Frank Moore which builds finitely generated R-modules
having a prescribed cohomological support set. The algorithm is based on a
theorem of mine and Avramov.