Rutgers MATH 560, Fall 2018.

Categories of modules, complexes and resolutions, derived functors, spectral sequences,...

daniel.krashen@rutgers.edu

- Modules: hom, tensor, injectives, projectives and flats
- Abelian categories
- Complexes, homology, resolutions
- Tor, Ext and other Derived functors
- Hypercohomology
- Spectral sequences
- Derived categories

- Group homology and cohomology
- Hoschild homology and cohomology
- Categories of sheaves and their cohomology
- Cech cohomology
- Lie algebra cohomology
- Simplicial methods
- Homotopical algebra
- Examples of spectral sequences and computations: Bicomplexes, hypercohomology, Grothendieck spectral sequence, Lyndon-Hoschild-Serre spectral sequence, exact couples, Leray-Serre spectral sequence,…