Quadratic Chabauty and Rational Points II: Generalised Height Functions on Selmer Varieties-Reference-Cited by-同舟云学术

Quadratic Chabauty and Rational Points II: Generalised Height Functions on Selmer Varieties

Published:2020-02-01 Issue:15 Volume:2021 Page:11923-12008
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Balakrishnan Jennifer S¹,Dogra Netan²

Affiliation:

1. Department of Mathematics and Statistics, Boston University, 111 Cummington Mall, Boston, MA 02215, USA

2. Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, OX2 6GG, UK

Abstract

Abstract We give new instances where Chabauty–Kim sets can be proved to be finite, by developing a notion of “generalised height functions” on Selmer varieties. We also explain how to compute these generalised heights in terms of iterated integrals and give the 1st explicit nonabelian Chabauty result for a curve $X/\mathbb{Q}$ whose Jacobian has Mordell–Weil rank larger than its genus.

Funder

National Science Foundation

Henry Luce Foundation

EPSRC

NWO/DIAMANT

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/article-pdf/2021/15/11923/39457965/rnz362.pdf

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