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An effective Chabauty--Kim theorem

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Jennifer Balakrishnan, Netan Dogra

Original languageEnglish
Pages (from-to)1057-1075
Issue number6
Published14 May 2019

King's Authors


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.

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