A non-archimedean definable Chow theorem

TL;DR

This paper establishes a non-archimedean analogue of a Chow theorem, showing that definable closed analytic subsets in non-archimedean settings are algebraic, extending classical complex algebraic geometry results.

Contribution

It introduces a non-archimedean version of Chow's theorem for definable sets, broadening the scope of algebraic geometry in non-archimedean contexts.

Findings

Definable closed analytic subsets are algebraic in non-archimedean settings.

Extends classical Chow theorem to non-archimedean geometry.

Bridges model theory and algebraic geometry in non-archimedean fields.

Abstract

Peterzil and Starchenko have proved the following surprising generalization of Chow's theorem: A closed analytic subset of a complex algebraic variety that is definable in an o-minimal structure, is in fact an algebraic subset. In this paper, we prove a non-archimedean analogue of this result.