Number Theory Seminar
Speaker: Steffen Müller (Groningen)
Title: Quadratic Chabauty
Abstract: By Faltings' theorem, a curve of genus at least 2 over the rationals has only finitely many rational points. However, computing the set of rational points explicitly for a given curve can be quite difficult. The Quadratic Chabauty method, developed by Balakrishnan and Dogra, is an instance of Kim's nonabelian extension of Chabauty's method that can sometimes be used for this purpose. I will discuss the application to several modular curves of interest in the classification of Galois representations of elliptic curves; this is joint work with Jennifer Balakrishnan, Netan Dogra, Jan Tuitman and Jan Vonk. I will also sketch a new and simplified approach to the Quadratic Chabauty method based on p-adic Arakelov theory, developed in joint work with Amnon Besser and Padmavathi Srinivasan.
The talk will be exclusively on Zoom. To receive the Zoom link, please contact one of the organizers if you are not on the Number Theory Seminar mailing list.