Submission date: 17 April 2012.

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 of bounded degree. We derive applications to semi-algebraic sets and recover a result of E. Hrushovski and F. Loeser which claims that points of Berkovich spaces give rise to definable types (a model-theoretic notion of tameness).

Mathematics Subject Classification: 14G22, 12J25, 14P10, 03C98

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Full text arXiv 1204.3417: pdf, ps.