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Definable subsets of a Berkovich curve

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Definable subsets of a Berkovich curve

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.

- Séminaire Géométrie et théorie des modèles

Détails :

Orateur / Oratrice : Pablo Cubides Kovacsics
Date : 15 février 2019
Horaire : 16h00 - 17h30
Lieu : ENS Salle W