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Séminaire Géométrie et théorie des modèles

Horaires : Le vendredi 15 février 2019, 16h - 17h30

Lieu : ENS, Salle W

Definable subsets of a Berkovich curve

Pablo Cubides Kovacsics (Dresden)

Let k be an algebraically closed complete rank 1 non-trivially valued field. Let X be an algebraic curve over k and let X^an be its analytification in the sense of Berkovich. We functorially associate to X^an a definable set X^S in a natural language. As a corollary, we obtain an alternative proof of a result of Hrushovski-Loeser about the iso-definability of curves. Our association being explicit allows us to provide a concrete description of the definable subsets of X^S: they correspond to radial sets. This is a joint work with Jérôme Poineau.

 

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