The Monsky-Washnitzer and the overconvergent realizations

Abstract

We construct the dagger realization functor for analytic motives over non-archimedean fields of mixed characteristic, as well as the Monsky-Washnitzer realization functor for algebraic motives over a discrete field of positive characteristic. In particular, the motivic language on the classic étale site provides a new direct definition of the overconvergent de Rham cohomology and rigid cohomology and shows that their finite dimensionality follows formally from the one of Betti cohomology for smooth projective complex varieties.

31 pages. Minor changes, Künneth formula added. Published online in International Mathematics Research Notices (2017)

References in corpus (2)

• The rigid syntomic ring spectrum
• Effective motives with and without transfers in characteristic $p$

Cited by in corpus (5)

• A motivic version of the theorem of Fontaine and Wintenberger
• Rigid cohomology via the tilting equivalence
• Rigidity for rigid analytic motives
• The Berkovich realization for rigid analytic motives
• A remark on crystalline cohomology