Cohen-Macaulay Representations

Cohen-Macaulay Representations
Author :
Publisher : American Mathematical Soc.
Total Pages : 390
Release :
ISBN-10 : 9780821875810
ISBN-13 : 0821875817
Rating : 4/5 (10 Downloads)

Book Synopsis Cohen-Macaulay Representations by : Graham J. Leuschke

Download or read book Cohen-Macaulay Representations written by Graham J. Leuschke and published by American Mathematical Soc.. This book was released on 2012-05-02 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (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 Krull-Remak-Schmidt Theorem on uniqueness of direct-sum decompositions and its failure for modules over local rings. Chapters 3-10 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 material--ADE/simple singularities, the double branched cover, Auslander-Reiten theory, and the Brauer-Thrall conjectures--is covered clearly and completely. Much of the content has never before appeared in book form. Examples include the representation theory of Artinian pairs and Burban-Drozd's related construction in dimension two, an introduction to the McKay correspondence from the point of view of maximal Cohen-Macaulay modules, Auslander-Buchweitz'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.


Cohen-Macaulay Representations Related Books

Cohen-Macaulay Representations
Language: en
Pages: 390
Authors: Graham J. Leuschke
Categories: Mathematics
Type: BOOK - Published: 2012-05-02 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

This book is a comprehensive treatment of the representation theory of maximal Cohen-Macaulay (MCM) modules over local rings. This topic is at the intersection
Maximal Cohen-Macaulay Modules over Cohen-Macaulay Rings
Language: en
Pages: 0
Authors: Y. Yoshino
Categories: Mathematics
Type: BOOK - Published: 1990-06-28 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

The purpose of these notes is to explain in detail some topics on the intersection of commutative algebra, representation theory and singularity theory. They ar
Representations of Algebras
Language: en
Pages: 212
Authors: P. Webb
Categories: Mathematics
Type: BOOK - Published: 1986-01-08 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

The latest developments in representation theory with emphasis on the representation type of finite-dimensional algebras.
Homological Theory of Representations
Language: en
Pages: 518
Authors: Henning Krause
Categories: Mathematics
Type: BOOK - Published: 2021-11-18 - Publisher: Cambridge University Press

DOWNLOAD EBOOK

Modern developments in representation theory rely heavily on homological methods. This book for advanced graduate students and researchers introduces these meth
Determinantal Rings
Language: en
Pages: 246
Authors: Winfried Bruns
Categories: Mathematics
Type: BOOK - Published: 2006-11-14 - Publisher: Springer

DOWNLOAD EBOOK

Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. Their study has attracted many prominent researchers