Finite Gorenstein representation type implies simple singularity
| dc.creator | Christensen, Lars Winther | |
| dc.creator | Piepmeyer, Greg | |
| dc.creator | Striuli, Janet | |
| dc.creator | Takahashi, Ryo | |
| dc.date | 2007-04-25 | |
| dc.date | 2008-02-22 | |
| dc.date.accessioned | 2026-07-07T09:22:10Z | |
| dc.date.available | 2026-07-07T09:22:10Z | |
| dc.description | 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. | |
| dc.description | Final version, to appear in Adv. Math. 14 pp | |
| dc.identifier | https://arxiv.org/abs/0704.3421 | |
| dc.identifier | http://arxiv.org/abs/0704.3421 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/155280 | |
| dc.subject | Commutative Algebra | |
| dc.subject | Representation Theory | |
| dc.subject | 14B05; 18G25; 13C14 | |
| dc.title | Finite Gorenstein representation type implies simple singularity | |
| dc.type | text |