AGANT SEMINAR
(Algebraic Geometry, Algebra and Number Theory Seminar)
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[x1,...,xn] by a regular sequence of
homogeneous polynomials f1,...,fc. 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[z1,...,zc]. The cone in
kc defined by annS(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.