We establish a tilting equivalence for rational, homotopy-invariant cohomology theories defined over non-archimedean analytic varieties. More precisely, we prove an 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 Kb 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 Kb are isomorphic.
A motivic version of the theorem of Fontaine and Wintenberger / A. Vezzani. - In: COMPOSITIO MATHEMATICA. - ISSN 0010-437X. - 155:1(2019 Jan), pp. 38-88. [10.1112/S0010437X18007595]
A motivic version of the theorem of Fontaine and Wintenberger
A. Vezzani
2019
Abstract
We establish a tilting equivalence for rational, homotopy-invariant cohomology theories defined over non-archimedean analytic varieties. More precisely, we prove an 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 Kb 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 Kb are isomorphic.File | Dimensione | Formato | |
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