Mathematics Colloquium - Prof. Jennifer Balakrishnan, University of Boston
When: | Tu 26-03-2024 16:00 - 17:00 |
Where: | 5161.0293 Bernoulliborg |
Title: Rational and mock rational points on curves
Abstract:
By a celebrated theorem of Faltings, a curve of genus 2 or more over the rationals has finitely many rational points. While Faltings' proof does not construct the finite set of rational points, Kim's nonabelian Chabauty program gives a finite superset of p-adic
points, known as the Chabauty--Kim sets. We describe the computation of the Chabauty--Kim sets in various settings and examine the mock rational points (those finitely many points that are not rational) that may arise in these sets. Throughout, we present a number of examples.