The Berkovich realization for rigid analytic motives
arXiv:1708.04284 · doi:10.1016/j.jalgebra.2019.02.026
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.
Minor changes, accepted for publication in J. Algebra, 19 pages