QUADRATIC CHABAUTY AND RATIONAL POINTS, I: p-ADIC HEIGHTS

摘要

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.