Title:

Computing rational points on curves using p-adic analysis

Abstract:

An algebraic curve over the rationals of genus at least 2 has only finitely many rational points, but provably computing them for a given curve can be extremely difficult. The idea of the method of Chabauty-Coleman, which can often be used to solve such problems, is to use p-adic analysis to cut out the rational points inside a larger space. I will discuss this approach and an extension thereof, which can be used in some cases where Chabauty-Coleman is not applicable. The talk will contain several examples, including a partial solution to a problem posed by Serre. This is joint work with Jennifer Balakrishnan, Netan Dogra, Jan Tuitman and Jan Vonk.

Location:

KdVI meeting room, room F3.20