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Preprint Number 523

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523. Ehud Hrushovski, François Loeser, Bjorn Poonen
Berkovich spaces embed in Euclidean spaces

Submission date: 24 October 2012.


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.

Mathematics Subject Classification: 14G22 (Primary) 54F50 (Secondary)

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Full text arXiv 1210.6485: pdf, ps.

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