(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.