Syllabus
This course will be about Cohen-Macaulay modules over local Cohen-Macaulay rings, with a view towards Auslander-Reiten sequences and what it means for such sequences to generate the relations of the Grothendieck group. Depending on time and interest, we may consider these questions in the generality of Exact categories which has applications to (Cohen-Macaulay) orders. (1) Recalling definitions of Cohen-Macaulay rings, (maximal)Cohen-Macaulay modules, Gorenstein rings. (2) Exact categories. (3) Auslander-Reiten sequences. (4) Functor categories, and the subcategories of finitely generated, and finitely presented functors. (5) Grothendieck groups. (6) When are the relations in the Grothendieck group generated by Auslander-Reiten sequences ?
Annotation
Non-repeated universal elective course.
In the academic year 2023/24:
This course will be about Cohen–Macaulay modules over local Cohen–Macaulay rings, with a view towards Auslander-Reiten sequences and what it means for such sequences to generate the relations of the Grothendieck group