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arXiv · 2301.11193

Linear and quadratic Chabauty for affine hyperbolic curves

Marius Leonhardt·Martin Lüdtke·J. Steffen Müller
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Abstract

We give sufficient conditions for finiteness of linear and quadratic refined Chabauty-Kim loci of affine hyperbolic curves. We achieve this by constructing depth $\leq 2$ quotients of the fundamental group, following a construction of Balakrishnan-Dogra in the projective case. We also apply Betts' machinery of weight filtrations to give unconditional explicit upper bounds on the number of S-integral points when our conditions are satisfied.

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Marius Leonhardt, Martin Lüdtke, J. Steffen Müller. 2023-01-26. Linear and quadratic Chabauty for affine hyperbolic curves. https://doi.org/10.1093/imrn%2Frnad185

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