Brauer-Thrall theory for maximal Cohen-Macaulay modules

Graham J. Leuschke; Roger Wiegand

doi:10.1007/978-1-4614-5292-8_18

Brauer-Thrall theory for maximal Cohen-Macaulay modules

Graham J. Leuschke, Roger Wiegand

Department of Mathematics

Research output: Chapter in Book/Entry/Poem › Chapter

3 Scopus citations

Abstract

The Brauer-Thrall Conjectures, now theorems, were originally stated for finitely generated modules over a finite-dimensional k-algebra. They say, roughly speaking, that infinite representation type implies the existence of lots of indecomposable modules of arbitrarily large k-dimension. These conjectures have natural interpretations in the context of maximal Cohen-Macaulay modules over Cohen-Macaulay local rings. This is a survey of progress on these transplanted conjectures.

Original language	English (US)
Title of host publication	Commutative Algebra
Subtitle of host publication	Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday
Publisher	Springer New York
Pages	577-592
Number of pages	16
ISBN (Electronic)	9781461452928
ISBN (Print)	1461452910, 9781461452911
DOIs	https://doi.org/10.1007/978-1-4614-5292-8_18
State	Published - Nov 1 2013

ASJC Scopus subject areas

General Mathematics

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10.1007/978-1-4614-5292-8_18

Cite this

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abstract = "The Brauer-Thrall Conjectures, now theorems, were originally stated for finitely generated modules over a finite-dimensional k-algebra. They say, roughly speaking, that infinite representation type implies the existence of lots of indecomposable modules of arbitrarily large k-dimension. These conjectures have natural interpretations in the context of maximal Cohen-Macaulay modules over Cohen-Macaulay local rings. This is a survey of progress on these transplanted conjectures.",

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AB - The Brauer-Thrall Conjectures, now theorems, were originally stated for finitely generated modules over a finite-dimensional k-algebra. They say, roughly speaking, that infinite representation type implies the existence of lots of indecomposable modules of arbitrarily large k-dimension. These conjectures have natural interpretations in the context of maximal Cohen-Macaulay modules over Cohen-Macaulay local rings. This is a survey of progress on these transplanted conjectures.

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ER -

Brauer-Thrall theory for maximal Cohen-Macaulay modules

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