CohenMacaulay representations
 Author/Creator
 Leuschke, Graham J., 1973
 Language
 English.
 Imprint
 Providence, R.I. : American Mathematical Society, c2012.
 Physical description
 xvii, 367 p. : ill ; 26 cm.
 Series
 Mathematical surveys and monographs ; no. 181.
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QA3 .A4 V.181
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Contributors
 Contributor
 Wiegand, Roger, 1943
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Contents

 Chapter 1. The KrullRemakSchmidt theorem
 Chapter 2. Semigroups of modules
 Chapter 3. Dimension zero
 Chapter 5. Invariant theory
 Chapter 6. Kleinian singularities and finite CM type
 Chapter 7. Isolated singularities and dimension two
 Chapter 8. The double branched cover
 Chapter 9. Hypersurfaces with finite CM type
 Chapter. 10. Ascent and descent
 Chapter 11. AuslanderBuchweitz theory
 Chapter 12. Totally reflexive modules
 Chapter 13. AuslanderReiten theory
 Chapter 14. Countable CohenMacaulay type
 Chapter 15. The BrauerThrall conjectures
 Chapter 16. Finite CM type in higher dimensions
 Chapter 17. Bounded CM type
 Appendix A.
 Basics and background
 Appendix B.
 Ramification theory.
 Publisher's Summary
 This book is a comprehensive treatment of the representation theory of maximal CohenMacaulay (MCM) modules over local rings. This topic is at the intersection of commutative algebra, singularity theory, and representations of groups and algebras. Two introductory chapters treat the KrullRemakSchmidt Theorem on uniqueness of directsum decompositions and its failure for modules over local rings. Chapters 310 study the central problem of classifying the rings with only finitely many indecomposable MCM modules up to isomorphism, i.e., rings of finite CM type. The fundamental materialADE/simple singularities, the double branched cover, AuslanderReiten theory, and the BrauerThrall conjecturesis covered clearly and completely. Much of the content has never before appeared in book form. Examples include the representation theory of Artinian pairs and BurbanDrozd's related construction in dimension two, an introduction to the McKay correspondence from the point of view of maximal CohenMacaulay modules, AuslanderBuchweitz's MCM approximation theory, and a careful treatment of nonzero characteristic. The remaining seven chapters present results on bounded and countable CM type and on the representation theory of totally reflexive modules.
(source: Nielsen Book Data)
Subjects
 Subject
 CohenMacaulay modules.
 Representations of rings (Algebra)
 Commutative algebra  Theory of modules and ideals  CohenMacaulay modules.
 Associative rings and algebras  Representation theory of rings and algebras  CohenMacaulay modules.
 Commutative algebra  Ring extensions and related topics  Étale and flat extensions; Henselization; Artin approximation.
 Commutative algebra  Theory of modules and ideals  Structure, classification theorems.
 Commutative algebra  Theory of modules and ideals  Module categories.
 Commutative algebra  Local rings and semilocal rings  Special types (CohenMacaulay, Gorenstein, Buchsbaum, etc.)
 Associative rings and algebras  Representation theory of rings and algebras  Representations of Artinian rings.
 Associative rings and algebras  Representation theory of rings and algebras  Representation type (finite, tame, wild, etc.)
 Associative rings and algebras  Representation theory of rings and algebras  AuslanderReiten sequences (almost split sequences) and AuslanderReiten quivers.
Bibliographic information
 Publication date
 2012
 Responsibility
 Graham J. Leuschke, Roger Wiegand.
 Series
 Mathematical surveys and monographs ; v. 181
 ISBN
 9780821875810
 0821875817