Berkovich spaces embed in Euclidean spaces

  • Ehud Hrushovski

    Hebrew University, Jerusalem, Israel
  • François Loeser

    Université Pierre et Marie Curie, Paris, France
  • Bjorn Poonen

    Massachusetts Institute of Technology, Cambridge, United States

Abstract

Let be a field that is complete with respect to a nonarchimedean absolute value such that has a countable dense subset. We prove that the Berkovich analytification of any -dimensional quasi-projective scheme over embeds in . If, moreover, the value group of is dense in and is a curve, then we describe the homeomorphism type of by using the theory of local dendrites.

Cite this article

Ehud Hrushovski, François Loeser, Bjorn Poonen, Berkovich spaces embed in Euclidean spaces. Enseign. Math. 60 (2014), no. 3/4, pp. 273–292

DOI 10.4171/LEM/60-3/4-4