Berkovich spaces embed in Euclidean spaces
Algebraic Geometry
2015-06-04 v1 General Topology
Number Theory
Abstract
Let K be a field that is complete with respect to a nonarchimedean absolute value such that K has a countable dense subset. We prove that the Berkovich analytification V^an of any d-dimensional quasi-projective scheme V over K embeds in R^{2d+1}. If, moreover, the value group of K is dense in R_{>0} and V is a curve, then we describe the homeomorphism type of V^an by using the theory of local dendrites.
Keywords
Cite
@article{arxiv.1210.6485,
title = {Berkovich spaces embed in Euclidean spaces},
author = {Ehud Hrushovski and François Loeser and Bjorn Poonen},
journal= {arXiv preprint arXiv:1210.6485},
year = {2015}
}
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15 pages