An effective Chabauty-Kim theorem
Number Theory
2019-05-15 v2 Algebraic Geometry
Abstract
The Chabauty--Kim method is a method for finding rational points on curves under certain technical conditions, generalising Chabauty's proof of the Mordell conjecture for curves with Mordell--Weil rank less than their genus. We show how the Chabauty--Kim method, when these technical conditions are satisfied in depth 2, may be applied to bound the number of rational points on a curve of higher rank. This provides a nonabelian generalisation of Coleman's effective Chabauty theorem.
Cite
@article{arxiv.1803.10102,
title = {An effective Chabauty-Kim theorem},
author = {Jennifer Balakrishnan and Netan Dogra},
journal= {arXiv preprint arXiv:1803.10102},
year = {2019}
}
Comments
Corrected statement of Theorem 1.2. Added an example