Stable local cohomology

ABSTRACT

For a module having a complete injective resolution, we define a stable version of local cohomology. This gives a functor to the stable category of Gorenstein injective modules. We show that in many ways this functor behaves like the usual local cohomology functor. Our main result is that when there is only one nonzero local cohomology module, there is a strong connection between that module and the stable local cohomology module; in fact, the latter gives a Gorenstein injective approximation of the former.

KEYWORDS:

• Complete resolutions
• local cohomology
• stable module category

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 13D02
• 13D45
• 13C11

Acknowledgements

First and foremost, many thanks are owed to my advisor Mark Walker, for countless hours of conversation and advice. Additionally, conversations with many individuals in the UNL department of mathematics have been very helpful; in particular, I would like to thank Luchezar Avramov, Srikanth Iyengar, Haydee Lindo, and Tom Marley. I would also like to thank the referee for helpful suggestions.