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Quadratic Chabauty and rational points I: p-adic heights

Published 4 Jan 2016 in math.NT and math.AG | (1601.00388v2)

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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