Algebraization of rigid analytic varieties and formal schemes via perfect complexes
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918501295325184 |
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| author | Montagnani, Matteo |
| author_facet | Montagnani, Matteo |
| contents | In this paper, we extend a theorem of Toën and Vaquié to the non-Archimedean and formal settings. More precisely, we prove that a smooth and proper rigid analytic variety is algebraizable if and only if its category of perfect complexes is smooth and proper. As a corollary, we deduce an analogous statement for formal schemes and demonstrate that, in general, the bounded derived category of coherent sheaves on a formal scheme is not smooth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13911 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraization of rigid analytic varieties and formal schemes via perfect complexes Montagnani, Matteo Algebraic Geometry In this paper, we extend a theorem of Toën and Vaquié to the non-Archimedean and formal settings. More precisely, we prove that a smooth and proper rigid analytic variety is algebraizable if and only if its category of perfect complexes is smooth and proper. As a corollary, we deduce an analogous statement for formal schemes and demonstrate that, in general, the bounded derived category of coherent sheaves on a formal scheme is not smooth. |
| title | Algebraization of rigid analytic varieties and formal schemes via perfect complexes |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2501.13911 |