A motivic version of the theorem of Fontaine and Wintenberger

Abstract

We prove the equivalence between the categories of motives of rigid analytic varieties over a perfectoid field $K$ of mixed characteristic and over the associated (tilted) perfectoid field $K^{♭}$ of equal characteristic. This can be considered as a motivic generalization of a theorem of Fontaine and Wintenberger, claiming that the Galois groups of $K$ and $K^{♭}$ are isomorphic. A main tool for constructing the equivalence is Scholze's theory of perfectoid spaces.

Stable version added. Accepted for publication. 46 pages

References in corpus (7)

• Relative p-adic Hodge theory, II: Imperfect period rings
• The Monsky-Washnitzer and the overconvergent realizations
• Rigid cohomology via the tilting equivalence
• T-model structures on chain complexes of presheaves
• Frobenius gauges and a new theory of p-torsion sheaves in characteristic p. I
• Effective motives with and without transfers in characteristic $p$
• The full faithfulness conjectures in characteristic p

Cited by in corpus (9)

• Relative p-adic Hodge theory, II: Imperfect period rings
• The six-functor formalism for rigid analytic motives
• Rigid cohomology via the tilting equivalence
• Effective motives with and without transfers in characteristic $p$
• Rigidity for rigid analytic motives
• Overconvergent global analytic geometry
• Homotopy theory of dg sheaves
• The Berkovich realization for rigid analytic motives
• The de Rham-Fargues-Fontaine cohomology