Boston University Number Theory Seminar

Boston University Number Theory Seminar – Spring 2020

Boundedness in families of projective varieties with applications to arithmetic hyperbolicity

Raymond van Bommel
(MIT)

Monday, January 27 at 4:15pm
111 Cummington Mall, MCS B31


Abstract

There exist different notions of hyperbolicity that have been conjectured to be equivalent. For example, a compact analytic space is called Brody hyperbolic, if there are no copies of the complex numbers inside it, and a proper algebraic variety X is called algebraically hyperbolic if the degree of all non-constant maps C -> X is bounded linearly in the genus of C. In this work, joint with Ariyan Javanpeykar and Ljudmila Kamenova, we provide evidence for the conjectural equivalence by studying how these notions behave in families of varieties. Moreover, we introduce a weaker notion of hyperbolicity and use it to prove new finiteness results for points on certain surfaces and semi-abelian varieties.