Back to Commutative Algebra Seminar: Spring 2015
Commutative Algebra Seminar
Date: Friday, Mar 6, 2015
Time: 3:10PM - 4:00PM
Location: LCB 222
Peder Thompson
University of Nebraska, Lincoln
Title |
Stable local cohomology |
Abstract |
Let R be a Gorenstein local ring, I an ideal in R, and M an R-module. The local cohohomology of M supported at I can be computed by applying the I-torsion functor to the injective resolution of M. Since R is Gorenstein, M has a complete injective resolution, so it is natural to ask what one gets by applying the I-torsion functor to it. Following this lead, we define stable local cohomology for modules with complete resolutions. This gives a functor to the stable category of Gorenstein injective modules. We show that in many ways this behaves like the usual local cohomology functor. Our main result is that when there is only one non-zero local cohomology module, there is strong connection between that and stable local cohomology; in fact, the latter gives a Gorenstein injective approximation of the former. |
Commutative Algebra