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 \(\mathbb{Q}\) or a quadratic number field. We accomplish this by studying the role of \(p\)-adic heights in explicit nona...

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Bibliographic Details
Published inarXiv.org
Main Authors Balakrishnan, Jennifer S, Dogra, Netan
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 01.05.2018
Subjects
Mathematics - Algebraic Geometry
Mathematics - Number Theory
Number theory
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1601.00388