Brauer-Thrall theory for maximal Cohen-Macaulay modules

Graham J. Leuschke, Roger Wiegand

Research output: ResearchChapter

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.

LanguageEnglish (US)
Title of host publicationCommutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday
PublisherSpringer New York
Pages577-592
Number of pages16
ISBN (Print)9781461452928, 1461452910, 9781461452911
DOIs
StatePublished - Nov 1 2013

Fingerprint

Cohen-Macaulay Module
Module
Cohen-Macaulay Ring
Representation Type
Local Ring
Finitely Generated
Imply
Algebra
Theorem
Interpretation
Context

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Leuschke, G. J., & Wiegand, R. (2013). Brauer-Thrall theory for maximal Cohen-Macaulay modules. In Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday (pp. 577-592). Springer New York. DOI: 10.1007/978-1-4614-5292-8_18

Brauer-Thrall theory for maximal Cohen-Macaulay modules. / Leuschke, Graham J.; Wiegand, Roger.

Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday. Springer New York, 2013. p. 577-592.

Research output: ResearchChapter

Leuschke, GJ & Wiegand, R 2013, Brauer-Thrall theory for maximal Cohen-Macaulay modules. in Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday. Springer New York, pp. 577-592. DOI: 10.1007/978-1-4614-5292-8_18
Leuschke GJ, Wiegand R. Brauer-Thrall theory for maximal Cohen-Macaulay modules. In Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday. Springer New York. 2013. p. 577-592. Available from, DOI: 10.1007/978-1-4614-5292-8_18
Leuschke, Graham J. ; Wiegand, Roger. / Brauer-Thrall theory for maximal Cohen-Macaulay modules. Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday. Springer New York, 2013. pp. 577-592
@inbook{ab3c6544a8f54a1d992e7c78a5a19f35,
title = "Brauer-Thrall theory for maximal Cohen-Macaulay modules",
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.",
author = "Leuschke, {Graham J.} and Roger Wiegand",
year = "2013",
month = "11",
doi = "10.1007/978-1-4614-5292-8_18",
isbn = "9781461452928",
pages = "577--592",
booktitle = "Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday",
publisher = "Springer New York",

}

TY - CHAP

T1 - Brauer-Thrall theory for maximal Cohen-Macaulay modules

AU - Leuschke,Graham J.

AU - Wiegand,Roger

PY - 2013/11/1

Y1 - 2013/11/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84929567416&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84929567416&partnerID=8YFLogxK

U2 - 10.1007/978-1-4614-5292-8_18

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

M3 - Chapter

SN - 9781461452928

SN - 1461452910

SN - 9781461452911

SP - 577

EP - 592

BT - Commutative Algebra: Expository Papers Dedicated to David Eisenbud on the Occasion of His 65th Birthday

PB - Springer New York

ER -