Reading Seminar on Homological algebra

Fall 2016

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 categories19.1-19.2 + Neeman, Triangulated Categories, Prop 1.6.8 Anna, Ruth
December 1 Spectral Sequences Ravi Vakil's introduction to spectral sequences Tim, Matt