On local rings without small Cohen-Macaulay algebras in mixed characteristic
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866908741936349184 |
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| author | Shimomoto, Kazuma Tavanfar, Ehsan |
| author_facet | Shimomoto, Kazuma Tavanfar, Ehsan |
| contents | For any $d\ge 4$, by deformation theory of schemes, we present examples of (complete or excellent) $d$-dimensional mixed characteristic normal local domains admitting no small Cohen-Macaulay algebra, but admitting instances of small (maximal) Cohen-Macaulay modules. It is also shown that a graded normal domain over a field whose Proj is an Abelian variety admits a graded small (maximal) Cohen-Macaulay module. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_12700 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | On local rings without small Cohen-Macaulay algebras in mixed characteristic Shimomoto, Kazuma Tavanfar, Ehsan Commutative Algebra Algebraic Geometry For any $d\ge 4$, by deformation theory of schemes, we present examples of (complete or excellent) $d$-dimensional mixed characteristic normal local domains admitting no small Cohen-Macaulay algebra, but admitting instances of small (maximal) Cohen-Macaulay modules. It is also shown that a graded normal domain over a field whose Proj is an Abelian variety admits a graded small (maximal) Cohen-Macaulay module. |
| title | On local rings without small Cohen-Macaulay algebras in mixed characteristic |
| topic | Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2109.12700 |