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.
|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|