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.File in questo prodotto:
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