Quadratic Chabauty and rational points II: Generalised height functions on Selmer varieties
Number Theory
2018-07-23 v2 Algebraic Geometry
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 first explicit nonabelian Chabauty result for a curve whose Jacobian has Mordell-Weil rank larger than its genus.
Keywords
Cite
@article{arxiv.1705.00401,
title = {Quadratic Chabauty and rational points II: Generalised height functions on Selmer varieties},
author = {Jennifer S. Balakrishnan and Netan Dogra},
journal= {arXiv preprint arXiv:1705.00401},
year = {2018}
}