Maximal Cohen-Macaulay Modules Over Cohen-Macaulay Rings

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Februar 2003



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.


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.


"In this excellently written book the author presents all the significant algebraic results on this topic...This book gives a careful, self-contained introduction to the theory of maximal Cohen-Macaulay modules readable by research students with thorough knowledge in commutative and general algebra; but it also may serve as a reference work." JUrgen Herzog, Mathematical Reviews
EAN: 9780521356947
ISBN: 0521356946
Untertitel: 'London Mathematical Society St'. New. Sprache: Englisch.
Erscheinungsdatum: Februar 2003
Seitenanzahl: 188 Seiten
Format: kartoniert
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