Number Theory Seminar

Speaker: Ariyan Javanpeykar (Mainz)

Title: Arithmetic, algebraic, and analytic hyperbolicity.

Abstract: The Lang-Vojta conjecture predicts that a complex algebraic variety is algebraically hyperbolic if and only if it is analytically hyperbolic if and only if it is arithmetically hyperbolic. This conjecture is known for the moduli space of polarized abelian varieties by work of Borel, Faltings, and Zuo. In this talk, I will explain this conjecture,  discuss its consequences for smooth hypersurfaces and Calabi-Yau varieties, and present a p-adic extension of the Lang-Vojta conjecture for the moduli space of polarized abelian varieties, using Scholze's theory of perfectoid spaces. Finally, I will discuss the conjecture for the moduli space of canonically polarized varieties.