Finite Gorenstein representation type implies simple singularity
Christensen, Lars Winther ; Piepmeyer, Greg ; Striuli, Janet ; Takahashi, Ryo
arXiv, 0704.3421 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2007-04-25
Classification:  Mathematics - Commutative Algebra,  Mathematics - Representation Theory,  14B05,  18G25,  13C14 
@article{0704.3421,
     author = {Christensen, Lars Winther and Piepmeyer, Greg and Striuli, Janet and Takahashi, Ryo},
     title = {Finite Gorenstein representation type implies simple singularity},
     journal = {arXiv},
     volume = {2007},
     number = {0},
     year = {2007},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0704.3421}
}

Christensen, Lars Winther; Piepmeyer, Greg; Striuli, Janet; Takahashi, Ryo. Finite Gorenstein representation type implies simple singularity. arXiv, Tome 2007 (2007) no. 0, . http://gdmltest.u-ga.fr/item/0704.3421/