A $p$-adic Simpson correspondence for singular rigid-analytic varieties
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866918500466950144 |
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| author | Cai, Hanlin Liu, Zeyu |
| author_facet | Cai, Hanlin Liu, Zeyu |
| contents | Let $C$ be a complete, algebraically closed non-archimedean extension of $\mathbb{Q}_p$, and $X$ be a proper rigid-analytic variety over $C$. We show that the category of pro-étale vector bundles on $X$ is equivalent to the category of Higgs bundles on the $\eh$-site of $X$, thereby generalizing the work of Faltings and Heuer to arbitrary proper rigid-analytic varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21418 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A $p$-adic Simpson correspondence for singular rigid-analytic varieties Cai, Hanlin Liu, Zeyu Algebraic Geometry Let $C$ be a complete, algebraically closed non-archimedean extension of $\mathbb{Q}_p$, and $X$ be a proper rigid-analytic variety over $C$. We show that the category of pro-étale vector bundles on $X$ is equivalent to the category of Higgs bundles on the $\eh$-site of $X$, thereby generalizing the work of Faltings and Heuer to arbitrary proper rigid-analytic varieties. |
| title | A $p$-adic Simpson correspondence for singular rigid-analytic varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2512.21418 |