A Study of quasi-Gorenstein rings II: Deformation of quasi-Gorenstein property
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866914359290101760 |
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| author | Shimomoto, Kazuma Taniguchi, Naoki Tavanfar, Ehsan |
| author_facet | Shimomoto, Kazuma Taniguchi, Naoki Tavanfar, Ehsan |
| contents | In the present article, we investigate the following deformation problem. Let $(R,\mathfrak m)$ be a local (graded local) Noetherian ring with a (homogeneous) regular element $y \in \mathfrak m$ and assume that $R/yR$ is quasi-Gorenstein. Then is $R$ quasi-Gorenstein? We give positive answers to this problem under various assumptions, while we present a counter-example in general. We emphasize that absence of the Cohen-Macaulay condition requires some delicate studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1810_03181 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | A Study of quasi-Gorenstein rings II: Deformation of quasi-Gorenstein property Shimomoto, Kazuma Taniguchi, Naoki Tavanfar, Ehsan Commutative Algebra Algebraic Geometry In the present article, we investigate the following deformation problem. Let $(R,\mathfrak m)$ be a local (graded local) Noetherian ring with a (homogeneous) regular element $y \in \mathfrak m$ and assume that $R/yR$ is quasi-Gorenstein. Then is $R$ quasi-Gorenstein? We give positive answers to this problem under various assumptions, while we present a counter-example in general. We emphasize that absence of the Cohen-Macaulay condition requires some delicate studies. |
| title | A Study of quasi-Gorenstein rings II: Deformation of quasi-Gorenstein property |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/1810.03181 |