Séminaire Géométries ICJ

Arithmetic hyperbolicity

by Ariyan Javanpeykar

Europe/Paris
112 (ICJ)

112

ICJ

1er étage bâtiment Braconnier, Université Claude Bernard Lyon 1 - La Doua
Description
The Green-Griffiths-Lang-Vojta conjectures relate the hyperbolicity of an algebraic variety to the finiteness of sets of "rational points" over number fields. For instance, it suggests a striking answer to the fundamental question "Why do some polynomial equations with integer coefficients have only finitely many solutions in the integers?". Namely, if the zeroes of such a system define a hyperbolic variety, then this system should have only finitely many integer solutions. In this talk I will explain how to verify some of the algebraic, analytic, and arithmetic predictions this conjecture makes. The talk will be a mixture of arithmetic geometry and complex geometry.