Preliminary Syllabus for Homological Algebra

Core Topics

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

Possible supplementary topics

• 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,…