Automatic meromorphy in non-archimedean geometry
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911048782577664 |
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| author | Ducros, Antoine |
| author_facet | Ducros, Antoine |
| contents | In this text we prove that if X is a reduced non-archimedean analytic space and f is a analytic function on a dense Zariski-open subspace of X whose zero-locus is closed in X, then f is a meromorphic function on X. As a corollary, we deduce that every invertible analytic function on the analytification of a reduced scheme of finite type over an affinoid algebra is algebraic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20915 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automatic meromorphy in non-archimedean geometry Ducros, Antoine Algebraic Geometry 14G22, 14G99 In this text we prove that if X is a reduced non-archimedean analytic space and f is a analytic function on a dense Zariski-open subspace of X whose zero-locus is closed in X, then f is a meromorphic function on X. As a corollary, we deduce that every invertible analytic function on the analytification of a reduced scheme of finite type over an affinoid algebra is algebraic. |
| title | Automatic meromorphy in non-archimedean geometry |
| topic | Algebraic Geometry 14G22, 14G99 |
| url | https://arxiv.org/abs/2407.20915 |