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Cohen-Macaulay Modules over Cohen-Macaulay Rings (London Mathematical Society Lecture Note Series)

ISBN: 0521356946



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Cohen Macaulay Modules over Cohen Macaulay Rings London Mathematical Society Lecture Note Series

Cohen-Macaulay Modules over Cohen-Macaulay Rings (London Mathematical Society Lecture Note Series)
Cambridge University Press | 1990-09-28 | ISBN: 0521356946 | 188 pages | PDF | 2 MB

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.

Contents
Chapter 1. Preliminaries 1
Chapter 2. AR sequences and irreducible morphisms 8
Chapter 3. Isolated singularities 16
Chapter 4. Auslander categories 25
Chapter 5. AR quivers 35
Chapter 6. The Brauer-Thrall theorem 44
Chapter 7. Matrix factorizations 54
Chapter 8. Simple singularities 60
Chapter 9. One-dimensional CM rings of finite representation type 69
Chapter 10. McKay graphs 85
Chapter 11. Two-dimensional CM rings of finite representation type 98
Chapter 12. Knorrer's periodicity 106
Chapter 13. Grothendieck groups 118
Chapter 14. CM modules on quadrics 124
Chapter 15. Graded CM modules on graded CM rings 135
Chapter 16. CM modules on toric singularities 143
Chapter 17. Homogeneous CM rings of finite representation type 161
Addenda 168
References 170

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