A Non-Archimedean Definable Chow Theorem

Explore a 45-minute lecture on the non-Archimedean definable Chow theorem, delivered by Abhishek Oswal from the Institute for Advanced Study. Delve into the world of algebraization theorems from o-minimality and their applications in Diophantine geometry and Hodge theory. Examine the definable Chow theorem by Peterzil and Starchenko, which states that closed analytic subsets of complex algebraic varieties, definable in an o-minimal structure, are algebraic subsets. Investigate the non-Archimedean analogue of this result, covering topics such as tame properties of o-minimal structures, p-adic semi-algebraic and subanalytic sets, rationality of Poincaré series, and non-Archimedean analytic geometry. Learn about tame structures, dimension theory, and the rigid subanalytic Riemann extension theorem. Conclude with a proof of a special case of the non-Archimedean definable Chow theorem.

Intro
Motivation
Examples
Tame properties of o-minimal structures
p-adic semi-algebraic and subanalytic sets
Rationality of Poincaré series
Non-archimedean analytic geometry
Tame structures
Dimension theory
Non-archimedean definable Chow
Rigid subanalytic Riemann extension theorem
Proof of a special case