The Berkovich realization for rigid analytic motives
Algebraic Geometry
2019-03-14 v2 Algebraic Topology
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.
Keywords
Cite
@article{arxiv.1708.04284,
title = {The Berkovich realization for rigid analytic motives},
author = {Alberto Vezzani},
journal= {arXiv preprint arXiv:1708.04284},
year = {2019}
}
Comments
Minor changes, accepted for publication in J. Algebra, 19 pages