Regular rings over valuation rings
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866914433322713088 |
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| author | Lyu, Shiji |
| author_facet | Lyu, Shiji |
| contents | Bertin (1972) defined regularity for coherent local rings, and Knaf (2004) studied the property for a local ring $A$ essentially finitely presented over a valuation ring $V$. We discuss several properties of this notion of regularity for such $A$, obtaining results parallel to results for regularity of Noetherian local rings. We include classical and modern topics: openness of loci, perfectoid big Cohen--Macaulay algebras, and cotangent complexes. We also give an application to Noetherian rings, showing a version of Kodaira's vanishing theorem in large enough residue characteristics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_29104 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Regular rings over valuation rings Lyu, Shiji Commutative Algebra Bertin (1972) defined regularity for coherent local rings, and Knaf (2004) studied the property for a local ring $A$ essentially finitely presented over a valuation ring $V$. We discuss several properties of this notion of regularity for such $A$, obtaining results parallel to results for regularity of Noetherian local rings. We include classical and modern topics: openness of loci, perfectoid big Cohen--Macaulay algebras, and cotangent complexes. We also give an application to Noetherian rings, showing a version of Kodaira's vanishing theorem in large enough residue characteristics. |
| title | Regular rings over valuation rings |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2603.29104 |