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.
Maximilian Hauck (Thu,) studied this question.
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