Finite Gorenstein representation type implies simple singularity

• Autores: Lars Winther Christensen , Greg Piepmeyer, Janet Striuli, Ryo Takahashi
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 218, Nº 4, 2008, págs. 1012-1026
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.03.005
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• Resumen

  • 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