We prove that the functor associating to a rigid analytic variety the singular complex of the underlying Berkovich topological space is motivic, and defines the maximal Artin quotient of a motive. We use this to generalize Berkovich's results on the weight-zero part of the étale cohomology of a variety defined over a non-archimedean valued field.

The Berkovich realization for rigid analytic motives / A. Vezzani. - In: JOURNAL OF ALGEBRA. - ISSN 0021-8693. - 527(2019 Jun 01), pp. 30-54. [10.1016/j.jalgebra.2019.02.026]

The Berkovich realization for rigid analytic motives

A. Vezzani
2019

Abstract

We prove that the functor associating to a rigid analytic variety the singular complex of the underlying Berkovich topological space is motivic, and defines the maximal Artin quotient of a motive. We use this to generalize Berkovich's results on the weight-zero part of the étale cohomology of a variety defined over a non-archimedean valued field.
Artin motives; Berkovich spaces; Etale cohomology; Motives; Rigid analytic spaces
Settore MAT/02 - Algebra
Settore MAT/03 - Geometria
1-giu-2019
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/771404
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