An effective Chabauty-Kim theorem
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Citation (published version)Jennifer Balakrishnan, Netan Dogra. 2019. "An effective Chabauty-Kim theorem." Compositio Mathematica, Volume 55, Issue 6, pp. 1057 - 1075. https://doi.org/10.1112/S0010437X19007243
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.