Number Theory Seminar

Conditionally on the Fontaine-Mazur, Hodge, and Tate conjectures, there is an algorithm that finds all rational points on any curve of genus at least 2 over a number field. The algorithm uses Faltings's original proof of the finiteness of rational points, along with an analytic bound on the degree of an isogeny due to Masser and Wüstholz. (Work in progress with Levent Alpoge.)