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

Abstract: The method of Chabauty and Coleman is a powerful method to determine rational points on curves whose Jacobian has the Mordell-Weil rank over $\mathbb{Q}$ (denoted by $r$) less than its genus (denoted by $g$). In this talk, we show how to construct a locally analytic function, using $p$-adic (Coleman-Gross) heights, that we use to compute integral points on certain even degree hyperelliptic curves when $r=g$. This is joint work with Steffen Müller.

Mathematics

Audience: researchers in the discipline

Greek Algebra & Number Theory Seminar