Math 582FB
Homological Algebra
James Zhang
Winter 2005, Monday/Wednesday/Friday 1:30
In the beginning of the course (about 3 weeks) we will cover the basic
theory in homological algebra: free modules, projective modules, injective
modules, complexes, the functors Hom and and tensor functors, and their
derived functions, Ext and Tor. We will also discuss some famous open
questions related to homological dimension.
We will then spend about 3 weeks covering some basis material about
triangulated categories, homotopy categories, and derived categories.
In the last part of the course (about 4 weeks) we will discuss several
theories involving derived categories:
- Belinson-Ginzburg-Soergel-Koszul derived equivalence.
- Rickard's tilting complexes and Morita derived equivalence.
- Yekutieli's dualizing complex for noncommutative rings.
- Bernstein-Gelfand-Gelfand correspondence.
- Grothendieck duality for schemes.