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15 August 2018 Quadratic Chabauty and rational points, I: p-adic heights
Jennifer S. Balakrishnan, Netan Dogra
Duke Math. J. 167(11): 1981-2038 (15 August 2018). DOI: 10.1215/00127094-2018-0013

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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Jennifer S. Balakrishnan. Netan Dogra. "Quadratic Chabauty and rational points, I: p-adic heights." Duke Math. J. 167 (11) 1981 - 2038, 15 August 2018. https://doi.org/10.1215/00127094-2018-0013

Information

Received: 3 May 2016; Revised: 9 March 2018; Published: 15 August 2018
First available in Project Euclid: 20 July 2018

zbMATH: 06941816
MathSciNet: MR3843370
Digital Object Identifier: 10.1215/00127094-2018-0013

Subjects:
Primary: 14G05
Secondary: 11G50 , 14G40

Keywords: non-Abelian Chabauty , p-adic heights , rational points on higher genus curves

Rights: Copyright © 2018 Duke University Press

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Vol.167 • No. 11 • 15 August 2018
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