CONTENTS ix §4. The index and applications to finite CM type 194 §5. Exercises 200 Chapter 12. Totally Reflexive Modules 203 §1. Stable Hom and Auslander transpose 203 §2. Complete resolutions 207 §3. Totally reflexive modules 209 §4. Exercises 215 Chapter 13. Auslander-Reiten Theory 217 §1. AR sequences 217 §2. AR quivers 224 §3. Examples 228 §4. Exercises 238 Chapter 14. Countable Cohen-Macaulay Type 241 §1. Structure 241 §2. Burban-Drozd triples 244 §3. Hypersurfaces of countable CM type 252 §4. Other examples 260 §5. Exercises 263 Chapter 15. The Brauer-Thrall Conjectures 267 §1. The Harada-Sai lemma 268 §2. Faithful systems of parameters 270 §3. Proof of Brauer-Thrall I 276 §4. Brauer-Thrall II 280 §5. Exercises 285 Chapter 16. Finite CM Type in Higher Dimensions 287 §1. Two examples 287 §2. Classification for homogeneous CM rings 293 §3. Exercises 295 Chapter 17. Bounded CM Type 297 §1. Hypersurface rings 297 §2. Dimension one 299 §3. Descent in dimension one 303 §4. Exercises 307 Appendix A. Basics and Background 309
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