Brauer-Thrall theory for maximal Cohen-Macaulay modules

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

Joint work with Roger Wiegand.


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.


Much of this material appears in our book, but here it is collected in one place, and explained a bit more clearly. The paper also lists some open questions.

Bibtex code:

@incollection {MR3051386,
    AUTHOR = {Leuschke, Graham J. and Wiegand, Roger},
     TITLE = {Brauer-{T}hrall theory for maximal {C}ohen-{M}acaulay modules},
 BOOKTITLE = {Commutative algebra},
     PAGES = {577--592},
 PUBLISHER = {Springer},
   ADDRESS = {New York},
      YEAR = {2013},
   MRCLASS = {13C14},
  MRNUMBER = {3051386},
       DOI = {10.1007/978-1-4614-5292-8_18},
       URL = {},