Maximal Cohen-Macaulay Modules over Cohen-Macaulay Rings

• 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. Knörrer'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." JÜrgen Herzog, Mathematical Reviews