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Title of Journal: Math Ann

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Abbravation: Mathematische Annalen

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Springer Berlin Heidelberg

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DOI

10.1016/0277-9536(95)00278-f

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1432-1807

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Polynomial approximation of Berkovich spaces and d

Authors: Jérôme Poineau
Publish Date: 2013/10/27
Volume: 358, Issue: 3-4, Pages: 949-970
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Abstract

We investigate affine Berkovich spaces over maximally complete fields and prove that they may be approximated by simpler spaces when the only functions we need to evaluate are polynomials with bounded degrees We derive applications to semialgebraic sets and recover a result of E Hrushovski and F Loeser claiming that points of Berkovich spaces give rise to definable types a modeltheoretic notion of tamenessIn 2010 I was given the opportunity to attend the summer conference of the MRC program on model theory of fields in Snowbird Resort Utah I would like to thank all the participants who explained the basics of model theory to me with much patience and insight I would also like to express my sincere gratitude to the referee for his precise and numerous comments and suggestions which contributed to improve the paper

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  24. On entropy, regularity and rigidity for convex representations of hyperbolic manifolds
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