On the relative Nullstellensatz in nonarchimedean geometry
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866914221513506816 |
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| author | Kedlaya, Kiran S. Mikami, Yutaro |
| author_facet | Kedlaya, Kiran S. Mikami, Yutaro |
| contents | We establish a relative version of the Nullstellensatz for algebras topologically of finite type over a given Banach Tate ring $A$, under the assumption that the corresponding statement holds for rational localizations of $A$. This applies in particular to pseudoaffinoid algebras and to the coordinate rings of affinoid subspaces of a Fargues--Fontaine curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_18183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the relative Nullstellensatz in nonarchimedean geometry Kedlaya, Kiran S. Mikami, Yutaro Algebraic Geometry Number Theory We establish a relative version of the Nullstellensatz for algebras topologically of finite type over a given Banach Tate ring $A$, under the assumption that the corresponding statement holds for rational localizations of $A$. This applies in particular to pseudoaffinoid algebras and to the coordinate rings of affinoid subspaces of a Fargues--Fontaine curve. |
| title | On the relative Nullstellensatz in nonarchimedean geometry |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2503.18183 |