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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.20382 |
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| _version_ | 1866917182547427328 |
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| author | Yu, Jiahong |
| author_facet | Yu, Jiahong |
| contents | Let $A$ be an affinoid integral domain over a non-Archimedean field $K$, and let $L$ be its field of fractions. We prove that the normalization of $A$ can be reconstructed from $L$ by taking the intersection of all maximal discrete valuation subrings. As a corollary, taking the field of fractions induces a fully faithful functor from the category of normal affinoid integral domains over $K$ to the category of field extensions of $K$. This provides another $p$-adic analogue of the Riemann Hebbarkeitssatz. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20382 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fields of Fractions in Rigid Geometry Yu, Jiahong Commutative Algebra Number Theory Let $A$ be an affinoid integral domain over a non-Archimedean field $K$, and let $L$ be its field of fractions. We prove that the normalization of $A$ can be reconstructed from $L$ by taking the intersection of all maximal discrete valuation subrings. As a corollary, taking the field of fractions induces a fully faithful functor from the category of normal affinoid integral domains over $K$ to the category of field extensions of $K$. This provides another $p$-adic analogue of the Riemann Hebbarkeitssatz. |
| title | Fields of Fractions in Rigid Geometry |
| topic | Commutative Algebra Number Theory |
| url | https://arxiv.org/abs/2512.20382 |