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arXiv · 1803.10102

An effective Chabauty-Kim theorem

Jennifer Balakrishnan·Netan Dogra
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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.

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Jennifer Balakrishnan, Netan Dogra. 2018-03-27. An effective Chabauty-Kim theorem. https://doi.org/10.1112/s0010437x19007243

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