Quadratic Chabauty and rational points I: p-adic heights
classification
🧮 math.NT
math.AG
keywords
chabautyexplicitheightsnonabelianpointsquadraticrationalaccomplish
read the original abstract
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 $\mathbb{Q}$ or a quadratic number field. We accomplish this by studying the role of $p$-adic heights in explicit nonabelian Chabauty.
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