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.
Rigid analytic reconstruction of Hyodo--Kato theory
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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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A motivic approach to rational $p$-adic cohomologies
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.