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arXiv · 1708.04284

The Berkovich realization for rigid analytic motives

Alberto Vezzani
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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 \'etale cohomology of a variety defined over a non-archimedean valued field.

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Alberto Vezzani. 2017-08-14. The Berkovich realization for rigid analytic motives. https://doi.org/10.1016/j.jalgebra.2019.02.026

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