Rigid analytic reconstruction of Hyodo--Kato theory

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.)

arXiv comment6th version, 88 pages. The definition of Hyodo--Kato cohomology is reverted to a previous version

References in corpus (3)

• Relative log convergent cohomology and relative rigid cohomology I
• Comparison between rigid syntomic and crystalline syntomic cohomology for strictly semistable log schemes with boundary
• Infinitesimal local study of formal schemes

Cited by in corpus (2)

• Hyodo-Kato theory with syntomic coefficients
• Poincaré duality for rigid analytic Hyodo--Kato theory