Arithmetic and algebraic hyperbolicity
Appears in collection : Entire curves, rational curves and foliations / Courbes entières, courbes rationnelles et feuilletages
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. I will present results that are joint work with Ljudmila Kamenova.
