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.
CITATION STYLE
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. https://doi.org/10.1007/978-1-4614-5292-8_18
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