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Cohen-Macaulay Modules over Cohen-Macaulay Rings (London Mathematical Society Lecture Note Series)
Posted on 2010-05-20
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More 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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