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Rational analytic syntomic cohomology | Synapse

April 21, 2026Open Access

Rational analytic syntomic cohomology

Key Points

This research aims to define rational analytic syntomification and explore its consequences in cohomology theory.
Defined the rational analytic syntomification for partially proper rigid-analytic varieties over Qp.
Established Poincaré duality and first Chern classes for the new cohomology.
Identified relationships between vector bundles on syntomified varieties and de Rham bundles on specific curves.
Demonstrated the effectiveness of Poincaré duality within the new cohomology framework.
Recover classical comparison theorems in p-adic Hodge theory.
Developed analogous results for constructions over C_p.

Abstract

We define and study the rational analytic syntomification X^Syn of a partially proper rigid-analytic variety X over Qₚ. We establish Poincaré duality and a theory of first Chern classes for the resulting cohomology theory, identify vector bundles on X^Syn with de Rham bundles on the Fargues--Fontaine curve of X^ and recover several classical comparison theorems in p-adic Hodge theory. We also develop analogues of our results and constructions over Cₚ.

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Cite this study

Maximilian Hauck (Thu,) studied this question.

synapsesocial.com/papers/69e7132bcb99343efc98cf1e — DOI: https://doi.org/10.48550/arxiv.2604.15193

Authors

M

Maximilian Hauck

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