UW Student Algebraic Geometry Seminar: Ting Gong

The distribution of rational points has been an old problem in number theory. Some of the milestones include the Mordell-Weil theorem and the Faltings’ theorem, explicitly explaining the structure of rational points on abelian varieties and on curves. In this talk, after reviewing basic definitions and constructions of hyperkähler varieties, we show that the rational points on hyperkähler varieties admitting one Lagrangian fibration is potentially dense for every known deformation family (over number fields), i.e. after a finite extension, the rational points on the variety is dense. This is based on my recent work with the same title.