Quadratic Chabauty and rational points I: p-adic heights

Netan Dogra; Jennifer Balakrishnan

doi:10.1215/00127094-2018-0013

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Quadratic Chabauty and rational points I: p-adic heights

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Netan Dogra, Jennifer Balakrishnan

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Original language	English
Pages (from-to)	1981-2038
Journal	Duke mathematical journal
Volume	167
Issue number	11
DOIs	https://doi.org/10.1215/00127094-2018-0013
Accepted/In press	2 Apr 2018
Published	20 Jul 2018
Additional links	https://arxiv.org/abs/1601.00388

King's Authors

Netan Dogra (Mathematics, Number Theory)

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 Q or a quadratic number field. We accomplish this by studying the role of p-adic heights in explicit non-Abelian Chabauty.

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Quadratic Chabauty and rational points I: p-adic heights

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