# A non-archimedean definable Chow theorem

# A non-archimedean definable Chow theorem

**Zoom link: ** **https://princeton.zoom.us/j/97126136441**

**Passw ord: **

**the three digit integer that is the cube of the sum of its digits**

In recent years, o-minimality has found some striking applications to diophantine geometry. The utility of o-minimal structures originates from the remarkably tame topological properties satisfied by sets definable in such structures. Despite the rigidity that it imposes, the theory is sufficiently flexible to allow for a range of analytic constructions. An illustration of this `tame' property is the following surprising generalization of Chow's theorem proved by Peterzil and Starchenko - A closed analytic subset of a complex algebraic variety that is also definable in an o-minimal structure, is in fact algebraic. While the o-minimal machinery aims to capture the archimedean order topology of the real line, it is natural to wonder if such a machinery can be set up over non-archimedean fields. In this talk, we shall explore a non-archimedean analogue of an o-minimal structure and a version of the definable Chow theorem in this context