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Cohen Macaulay modules over Cohen Macaulay rings

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The purpose of these notes is to explain in detail some topics on the intersection of commutative algebra, representation theory and singularity theory. They are based on lectures given in Tokyo, but also contain new research. It is the first cohesive account of the area and will provide a useful synthesis of recent research for algebraists.

Author(s): Yuji Yoshino
Series: London Mathematical Society lecture note series, 146
Publisher: Cambridge University Press
Year: 1990

Language: English
Pages: 188
City: Cambridge
Tags: Cohen-Macaulay rings;Cohen-Macaulay modules

1. Preliminaries
2. AR sequences and irreducible morphisms
3. Isolated singularities
4. Auslander categories
5. AR quivers
6. The Brauer-Thrall theorem
7. Matrix factorizations
8. Simple singularities
9. One-dimensional Cm rings of finite representation type
10. McKay graphs
11. Two-dimensional CM rings of finite representation type
12. Knorrer's periodicity
13. Grothendieck groups
14. CM modules on quadrics
15. Graded CM modules on graded CM rings
16. CM modules on toric singularities
17. Homogeneous CM rings of finite representation type
Addenda
References.