Brauer-Thrall theory for maximal Cohen-Macaulay modules

2012/11/14 by Leuschke, Graham J., Wiegand, Roger
#13C14 #13H10 #13J10 #16G30 (Secondary) #16G50 #16G60 (Primary) 13C05 #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1211.3172

Abstract

The Brauer-Thrall Conjectures, now theorems, were originally stated for finitely generated modules over a finite-dimensional \sk-algebra. They say, roughly speaking, that infinite representation type implies the existence of lots of indecomposable modules of arbitrarily large \sk-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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