Finite Gorenstein representation type implies simple singularity

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Let R be a commutative noetherian local ring and consider the set of isomorphism classes of indecomposable totally reflexive R-modules. We prove that if this set is finite, then either it has exactly one element, represented by the rank 1 free module, or R is Gorenstein and an isolated singularity (if R is complete, then it is even a simple hypersurface singularity). The crux of our proof is to argue that if the residue field has a totally reflexive cover, then R is Gorenstein or every totally reflexive R-module is free.
Final version, to appear in Adv. Math. 14 pp

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Commutative Algebra, Representation Theory, 14B05; 18G25; 13C14

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http://salesiana.dossiersoluciones.com/handle/123456789/155280

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0704.3421
 http://arxiv.org/abs/0704.3421

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arXiv