Berkovich spaces embed in Euclidean spaces

Berkovich spaces embed in Euclidean spaces

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...

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Bibliographic Details
Main Authors: Hrushovski, Ehud (Author), Loeser, François (Author), Poonen, Bjorn (Contributor)
Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
Format: Article
Language:English
Published: European Mathematical Society Publishing House, 2017-01-05T16:08:19Z.
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Summary: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.

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