Class Notes for Math 918: Local Cohomology, Instructor Tom Marley

Authors

Laura Lynch, University of Nebraska-LincolnFollow

Date of this Version

2010

Comments

These notes were not based off of the course I took, but rather from Tom Marley's lecture notes when he had taught it years earlier.

Abstract

Topics include: Injective Module, Basic Properties of Local Cohomology Modules, Local Cohomology as a Cech Complex, Long exact sequences on Local Cohomology, Arithmetic Rank, Change of Rings Principle, Local Cohomology as a direct limit of Ext modules, Local Duality, Chevelley’s Theorem, Hartshorne- Lichtenbaum Vanishing Theorem, Falting’s Theorem.