This will be an introduction to Homological Algebra. We will follow Eisenbud's book "Commutative Algebra with a view towards Algebraic Geometry" and cover topics including resolutions and derived functors, Tor and Ext, flatness, and Koszul complexes.
Schedule: Every Thursday, 11am-12pm, JCMB 6207
Students taking the class for credit: You will be asked to write down one relevant exercise per week (of your choosing) and to give at least one - ideally two - half-hour talks.
Tentative Schedule:
| Day | Topics | Assigned Reading | Speakers |
|---|---|---|---|
| October 7 | Flatness, projective modules | 6.0/6.1, A3.1-3.3 | - |
| October 14 | Tor and flatness, constructions with complexes | 6.2/6.3, A3.5-3.8 | - |
| October 20 | More Tor and flatness, derived functors | 6.4, A3.9-3.10 | - |
| October 27 | Injective complexes and Ext | A3.4 & 3.11 | - |
| November 3 | Koszul complexes | 17.1 & 17.2 | Ruth, Fatemeh |
| November 10 | No seminar this week | - | - |
| November 17 | Derived and triangulated categories | Huybrechts, pp. 11-15, 27-49 | Fatemeh, Anna |
| November 24 | Hilbert syzygy theorem + Colimits in triangulated categories | 19.1-19.2 + Neeman, Triangulated Categories, Prop 1.6.8 | Anna, Ruth |
| December 1 | Spectral Sequences | Ravi Vakil's introduction to spectral sequences | Tim, Matt |