Duality for Arithmetic $p$-adic Pro-étale Cohomology of Analytic Spaces
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866908406644736000 |
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| author | Li, Zhenghui |
| author_facet | Li, Zhenghui |
| contents | Let $K$ be a finite extension of $\mathbb{Q}_p$. We prove that the arithmetic $p$-adic pro-étale cohomology of smooth partially proper spaces over $K$ satisfies a duality, as conjectured by Colmez, Gilles and Nizioł. We derive it from the geometric duality on the Fargues-Fontaine curve by Galois descent techniques of Fontaine. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11786 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duality for Arithmetic $p$-adic Pro-étale Cohomology of Analytic Spaces Li, Zhenghui Algebraic Geometry Number Theory 14F30 Let $K$ be a finite extension of $\mathbb{Q}_p$. We prove that the arithmetic $p$-adic pro-étale cohomology of smooth partially proper spaces over $K$ satisfies a duality, as conjectured by Colmez, Gilles and Nizioł. We derive it from the geometric duality on the Fargues-Fontaine curve by Galois descent techniques of Fontaine. |
| title | Duality for Arithmetic $p$-adic Pro-étale Cohomology of Analytic Spaces |
| topic | Algebraic Geometry Number Theory 14F30 |
| url | https://arxiv.org/abs/2412.11786 |