Article contents
An effective Chabauty–Kim theorem
Published online by Cambridge University Press: 14 May 2019
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.
MSC classification
- Type
- Research Article
- Information
- Copyright
- © The Authors 2019
Footnotes
Balakrishnan is supported in part by NSF grant DMS-1702196, the Clare Boothe Luce Professorship (Henry Luce Foundation), and Simons Foundation grant #550023.
References
- 9
- Cited by