Topics in Commutative Algebra Seminar


I will keep a schedule of what I hope to cover in the seminar on this page. I will also post some useful resources. This is Not designed to be an introductory course/seminar and I will be assuming a first course in commutative and homological algebra. I have notes on my webpage here that constitute the prerequisites I am assuming. If you see something you don't recognize, you might be able to find an answer here.

I will be adding to these notes as we go, starting with depth. My goal is to eventually talk about local cohomology and some of the interesting open problems regarding it. I'll update this as we go along.

Depth Notes
Injective Modules Notes
Local Cohomology Notes Applications and Generalizations Notes

Date Topic
9/29Depth and Vanishing of Ext
10/6Koszul Complex and Free Resolutions
10/13Cohen-Macaulay Rings and Modules
10/20Hartshorne's Connectedness Theorem and Injective Envelopes
10/27Matlis Duality
11/3Minimal Injective Resolutions
11/10Gorenstein Rings
11/174 Definitions of Local Cohomology
11/24No Seminar - Thanksgiving
12/1Local Duality
1/19Hartshorne-Lichtenbaum Vanishing Theorem
1/26Falting's Connectedness Theorem
2/2Infinite Free Resolutions - Ines takes over
Last Updated: 1/26/2011