Berkovich spaces embed in Euclidean spaces

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.

15 pages

Cited by in corpus (4)

• Topological properties of Wazewski dendrite groups
• Topology of Spaces of Valuations and Geometry of Singularities
• Ultrametric properties for valuation spaces of normal surface singularities
• Links of sandwiched surface singularities and self-similarity