University of Oxford
Coleman integration and integral points on hyperelliptic curves
We will discuss explicit computations of p-adic line integrals (Coleman integrals) on hyperelliptic curves and some applications. We will give examples of iterated Coleman integrals present in Kim’s nonabelian Chabauty program. Moreover, we will discuss recent applications of using these integrals to find integral points on hyperelliptic curves. We use this to give a Chabauty-like method for computing p-adic approximations to integral points on such curves when the Mordell–Weil rank of the Jacobian equals the genus. This is joint work with Amnon Besser and Steffen Müller.