Graham J. Leuschke and Roger Wiegand
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.
In: Commutative algebra (expository papers dedicated to David Eisenbud on the occasion of his 65th birthday), 577–592, Springer, New York, 2013.
DOI: 10.1007/978-1-4614-5292-8_18