QCI

Quadratic Chabauty and rational points. I: p-adic heights. We give the first explicit examples beyond the Chabauty-Coleman method where Kim’s nonabelian Chabauty program determines the set of rational points of a curve defined over ℚ or a quadratic number field. We accomplish this by studying the role of p-adic heights in explicit non-abelian Chabauty.