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Brauer–Thrall Theory for Maximal Cohen–Macaulay Modules

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Commutative Algebra

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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Acknowledgments

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. Department of Mathematics, Syracuse University, Syracuse, NY, 13244, USA

    Graham J. Leuschke

  2. Department of Mathematics, University of Nebraska–Lincoln, Lincoln, NE, 68588, USA

    Roger Wiegand

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  1. Graham J. Leuschke
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Correspondence to Roger Wiegand .

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  1. Cornell University, 547 Malott Hall, Ithaca, 14853, New York, USA

    Irena Peeva

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Leuschke, G.J., Wiegand, R. (2013). Brauer–Thrall Theory for Maximal Cohen–Macaulay Modules. In: Peeva, I. (eds) Commutative Algebra. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-5292-8_18

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