Géométrie, Algèbre, Dynamique et Topologie

Arithmetic and algebraic hyperbolicity

by Ariyan JAVANPEYKAR (Univ. de Mayence)

Europe/Paris
Salle 318 (IMB)

Salle 318

IMB

Description

The Green-Griffiths-Lang-Vojta conjectures relate the hyperbolicity of an algebraic variety to the finiteness of sets of "rational points". 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.