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Rigid analytic reconstruction of Hyodo--Kato theory

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arxiv 1907.10964 v6 pith:QJ4FEUQ6 submitted 2019-07-25 math.NT

Veronika Ertl , Kazuki Yamada This is my paper · ORCID
classification math.NT
keywords hyodo--katocohomologychoiceconstructionrigidadicanalyticbranch
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abstract

We give a new and very intuitive construction of Hyodo--Kato cohomology and the Hyodo--Kato map, based on logarithmic rigid cohomology. We show that it is independent of the choice of a uniformiser and study its dependence on the choice of a branch of the $p$-adic logarithm. Moreover, we show the compatibility with the classical construction of Hyodo--Kato cohomology and the Hyodo--Kato map.)

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  1. A motivic approach to rational $p$-adic cohomologies

    math.AG 2025-08 conditional novelty 4.0 of 10

    Smooth complete intersections in projective toric varieties over p-adic fields satisfy the p-adic weight-monodromy conjecture, here re-proven through motivic nearby cycles and a monodromy-category equivalence.

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