Mathematics > Algebraic Geometry
arXiv:2604.15193 (math)
[Submitted on 16 Apr 2026 (v1), last revised 11 Jun 2026 (this version, v2)]
Abstract: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 $\mathbb{C}_p$.
Submission history
From: Maximilian Hauck [view email]
[v1]
Thu, 16 Apr 2026 16:23:32 UTC (196 KB)
[v2]
Thu, 11 Jun 2026 12:44:04 UTC (197 KB)
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