An algebraic characterisation of non-Archimedean Stein spaces
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912740952506368 |
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| author | Biesbrouck, Tom |
| author_facet | Biesbrouck, Tom |
| contents | We introduce Liu algebras as Banach algebras which are 'locally affinoid', and define non-Archimedean Stein algebras as suitable inverse limits of these. We show that this gives rise to a complete functorial characterisation of non-Archimedean Liu and Stein spaces as Berkovich spectra of their respective algebras, thereby resolving a conjecture of Michael Temkin. This can be interpreted as a non-Archimedean analytic version of Serre's criterion for affineness. Furthermore, we prove a criterion that distinguishes affinoid algebras within the category of Liu algebras, answering another conjecture of Temkin. We also prove a generalisation of the Gerritzen-Grauert Theorem for non-Archimedean Stein spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_01871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An algebraic characterisation of non-Archimedean Stein spaces Biesbrouck, Tom Algebraic Geometry We introduce Liu algebras as Banach algebras which are 'locally affinoid', and define non-Archimedean Stein algebras as suitable inverse limits of these. We show that this gives rise to a complete functorial characterisation of non-Archimedean Liu and Stein spaces as Berkovich spectra of their respective algebras, thereby resolving a conjecture of Michael Temkin. This can be interpreted as a non-Archimedean analytic version of Serre's criterion for affineness. Furthermore, we prove a criterion that distinguishes affinoid algebras within the category of Liu algebras, answering another conjecture of Temkin. We also prove a generalisation of the Gerritzen-Grauert Theorem for non-Archimedean Stein spaces. |
| title | An algebraic characterisation of non-Archimedean Stein spaces |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.01871 |