An effective Chabauty-Kim theorem

Author: 

Balakrishnan, J
Dogra, N

Publication Date: 

14 May 2019

Journal: 

Compositio Mathematica

Last Updated: 

2020-06-12T14:33:02.287+01:00

Issue: 

6

Volume: 

155

DOI: 

10.1112/S0010437X19007243

page: 

1057-1075

abstract: 

The Chabauty–Kim method allows one to find 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 non-abelian generalisation of Coleman’s effective Chabauty theorem.

Symplectic id: 

983813

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article