Time and Place:
Time: Wednesday, 12:00 – 14:00
Place: Math Building (no. 58), room 201
or Zoom – TBA
Course Topics: (as much as time permits)
Review of prior material. On rings, ideals and modules (including noncommutative rings).
Categories and functors. Emphasis on linear categories. (This topic will be introduced gradually, as we go along.)
Universal constructions. Free modules, products, direct sums, polynomial rings.
Tensor products. Definition, construction and properties.
Exactness. Exact sequences and functors.
Special modules. Projective, injective and flat modules.
Complexes of modules. Operations on complexes, homotopies, the long exact cohomology sequence.
Resolutions. Projective, flat and injective resolutions.
Left and right derived functors. Applications to commutative algebra.
Further applications of derived functors. Classification problems, extensions.
(Some of the material might move to the subsequent course “Commutative Algebra”)
For an updated syllabus and course requirements see the course web page
- Categories and functors: natural transformations, equivalence, adjoint functors, additive functors, exactness.
- Derived functors: projective, injective and flat modules; resolutions, the functors $Ext$ and $Tor$; examples and applications.
- Nonabelian cohomology and its applications.
Requirements and grading
see course web page