The étale open topology over the fraction field of a henselian local domain
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866912082267471872 |
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| author | Johnson, Will Walsberg, Erik Ye, Jinhe |
| author_facet | Johnson, Will Walsberg, Erik Ye, Jinhe |
| contents | Suppose that $R$ is a local domain with fraction field $K$. If $R$ is Henselian then the $R$-adic topology over $K$ refines the étale open topology. If $R$ is regular then the étale open topology over $K$ refines the $R$-adic topology. In particular the étale open topology over $L((t_1,\ldots,t_n))$ agrees with the $L[[t_1,\ldots,t_n]]$-adic topology for any field $L$ and $n \ge 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_01868 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The étale open topology over the fraction field of a henselian local domain Johnson, Will Walsberg, Erik Ye, Jinhe Algebraic Geometry Commutative Algebra Logic Suppose that $R$ is a local domain with fraction field $K$. If $R$ is Henselian then the $R$-adic topology over $K$ refines the étale open topology. If $R$ is regular then the étale open topology over $K$ refines the $R$-adic topology. In particular the étale open topology over $L((t_1,\ldots,t_n))$ agrees with the $L[[t_1,\ldots,t_n]]$-adic topology for any field $L$ and $n \ge 1$. |
| title | The étale open topology over the fraction field of a henselian local domain |
| topic | Algebraic Geometry Commutative Algebra Logic |
| url | https://arxiv.org/abs/2108.01868 |