Bound on the number of rational points on curves

Abstract: Mazur conjectured, after Faltings’s proof of the Mordell conjecture, that the number of rational points on a curve is bounded from above by the genus, the degree of the number field and the Mordell-Weil rank. In this talk I will explain the proof of this conjecture. This is joint work with Vesselin Dimitrov and Philipp Habegger.

algebraic geometrynumber theory

Audience: researchers in the topic

UCSB Seminar on Geometry and Arithmetic