Linear and Quadratic Chabauty for Affine Hyperbolic Curves

Marius Leonhardt, Martin Lüdtke*, Steffen Müller

*Corresponding author for this work

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We give sufficient conditions for finiteness of linear and quadratic refined Chabauty-Kim loci of affine hyperbolic curves. We achieve this by constructing depth ≤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.
Original languageEnglish
Pages (from-to)18752–18780
Number of pages29
JournalInternational Mathematics Research Notices
Issue number21
Early online date15-Aug-2023
Publication statusPublished - Nov-2023

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