Berkovich spaces embed in Euclidean spaces
Author(s)
Hrushovski, Ehud; Loeser, François; Poonen, Bjorn
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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[superscript an] of any d-dimensional quasi-projective scheme V over K embeds in R[superscrip 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[superscript an] by using the theory of local dendrites.
Date issued
2014Department
Massachusetts Institute of Technology. Department of MathematicsJournal
L’Enseignement Mathématique
Publisher
European Mathematical Society Publishing House
Citation
Hrushovski, Ehud, François Loeser, and Bjorn Poonen. “Berkovich Spaces Embed in Euclidean Spaces.” L’Enseignement Mathématique 60.3 (2014): 273–292.
Version: Original manuscript
ISSN
0013-8584