MIT Number Theory Seminar

Tuesday, December 10, 2019 at 4:30pm to 5:30pm

Room 2-143 -- MIT-Dept. of Mathematics, 77 Mass. Ave., Cambridge, MA

SPEAKER:  Abhishek Oswal (University of Toronto)

TITLE:  A non-archimedean definable Chow theorem


O-minimality has had some striking applications to number theory.  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 prove a version of the definable Chow theorem in this context.

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