Year: 2015
Type: article
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^{\mathrm {an}} of any d -dimensional quasi-projective scheme V over K embeds in \mathbb R^{2d+1} . If, moreover, the value group of K is dense in \mathbb R_{>0} and V is a curve, then we describe the homeomorphism type of V^{\mathrm {an}} by using the theory of local dendrites.
Source: L’Enseignement Mathématique
DOI: 10.4171/lem/60-3/4-4
Authors: Ehud Hrushovski, François Loeser, Bjorn Poonen
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2106584827