Brauer–Thrall Theory for Maximal Cohen–Macaulay Modules

  • Graham J. Leuschke
  • Roger WiegandEmail author


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.


Local Ring Indecomposable Module Minimal Prime Ideal Hypersurface Singularity Principal Ideal Ring 
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Research for this work was partially supported by NSF grant DMS-0902119 (GJL) and by a Simons Foundation Collaboration Grant (RW).


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Authors and Affiliations

  1. 1.Department of MathematicsSyracuse UniversitySyracuseUSA
  2. 2.Department of MathematicsUniversity of Nebraska–LincolnLincolnUSA

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