Rational points: Curves and beyond

Abstract: In 1985, Coleman, building on Chabauty's work from 1941, established an upper bound for the number of rational points of curves satisfying certain conditions. In this talk, I will present the first generalization of this method to higher dimensions, specifically to the case of surfaces. This is joint work with Hector Pasten. Furthermore, I will discuss recent work with Jennifer Balakrishnan, in which we provide explicit examples of surfaces that demonstrate the effectiveness of the method developed by H. Pasten and me. Specifically, we show that there are surfaces for which the obtained bound is sharp.

Finally, I will present joint work with Natalia García-Fritz, where we prove that a certain family of surfaces has a uniformly bounded number of rational points. In other words, the same upper bound applies to all surfaces in the family.

algebraic geometrynumber theory

Audience: researchers in the topic

Boston University Number Theory Seminar