Berkovich spaces embed in Euclidean spaces
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Poonen_Berkovich spaces.pdf
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233.31 KB
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Author(s)
Hrushovski, Ehud
Loeser, François
Poonen, Bjorn
Date Issued
2014
Journal
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
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[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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.4171/LEM/60-3/4-4
