Connectedness and integrally closed local overrings of two-dimensional regular local rings
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911919310372864 |
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| author | Heinzer, William Loper, K. Alan Olberding, Bruce Toeniskoetter, Matt |
| author_facet | Heinzer, William Loper, K. Alan Olberding, Bruce Toeniskoetter, Matt |
| contents | Let $D$ be a two-dimensional regular local ring. We prove there is a one-to-one correspondence between closed connected sets in the space of valuation overrings of $D$ that dominate $D$ and the integrally closed local overrings of $D$ that are not essential valuation rings or divisorial valuation rings of $D$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_10966 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Connectedness and integrally closed local overrings of two-dimensional regular local rings Heinzer, William Loper, K. Alan Olberding, Bruce Toeniskoetter, Matt Commutative Algebra 13A18, 13H05 Let $D$ be a two-dimensional regular local ring. We prove there is a one-to-one correspondence between closed connected sets in the space of valuation overrings of $D$ that dominate $D$ and the integrally closed local overrings of $D$ that are not essential valuation rings or divisorial valuation rings of $D$. |
| title | Connectedness and integrally closed local overrings of two-dimensional regular local rings |
| topic | Commutative Algebra 13A18, 13H05 |
| url | https://arxiv.org/abs/2406.10966 |