Rational analytic syntomic cohomology
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917414206177280 |
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| author | Hauck, Maximilian |
| author_facet | Hauck, Maximilian |
| contents | We define and study the rational analytic syntomification $X^{\mathrm{Syn}}$ of a partially proper rigid-analytic variety $X$ over $\mathbb{Q}_p$. We establish Poincaré duality and a theory of first Chern classes for the resulting cohomology theory, identify vector bundles on $X^{\mathrm{Syn}}$ with de Rham bundles on the Fargues--Fontaine curve of $X^{\diamondsuit}$ and recover several classical comparison theorems in $p$-adic Hodge theory. We also develop analogues of our results and constructions over $\mathbb{C}_p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15193 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rational analytic syntomic cohomology Hauck, Maximilian Algebraic Geometry Number Theory We define and study the rational analytic syntomification $X^{\mathrm{Syn}}$ of a partially proper rigid-analytic variety $X$ over $\mathbb{Q}_p$. We establish Poincaré duality and a theory of first Chern classes for the resulting cohomology theory, identify vector bundles on $X^{\mathrm{Syn}}$ with de Rham bundles on the Fargues--Fontaine curve of $X^{\diamondsuit}$ and recover several classical comparison theorems in $p$-adic Hodge theory. We also develop analogues of our results and constructions over $\mathbb{C}_p$. |
| title | Rational analytic syntomic cohomology |
| topic | Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2604.15193 |