Quadratic Chabauty for integral points and p-adic heights on even degree hyperelliptic curves

Abstract: In this talk, we show how to construct p-adic (Coleman-Gross) heights on even degree hyperelliptic curves, more precisely, its local component above p. Using heights, we construct a locally analytic function that we use to compute integral points on certain even degree hyperelliptic curves whose Jacobian has Mordell-Weil rank over Q equal to the genus. This is joint work with Steffen Müller.

algebraic geometrynumber theory

Audience: researchers in the topic

UCSB Seminar on Geometry and Arithmetic