Duke Mathematical Journal

Quadratic Chabauty and rational points, I: p-adic heights

Jennifer S. Balakrishnan and Netan Dogra

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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.

Article information

Source
Duke Math. J., Volume 167, Number 11 (2018), 1981-2038.

Dates
Received: 3 May 2016
Revised: 9 March 2018
First available in Project Euclid: 20 July 2018

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1532073621

Digital Object Identifier
doi:10.1215/00127094-2018-0013

Mathematical Reviews number (MathSciNet)
MR3843370

Zentralblatt MATH identifier
06941816

Subjects
Primary: 14G05: Rational points
Secondary: 11G50: Heights [See also 14G40, 37P30] 14G40: Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]

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

Citation

Balakrishnan, Jennifer S.; Dogra, Netan. Quadratic Chabauty and rational points, I: $p$ -adic heights. Duke Math. J. 167 (2018), no. 11, 1981--2038. doi:10.1215/00127094-2018-0013. https://projecteuclid.org/euclid.dmj/1532073621


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