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Linear and quadratic chabauty for affine hyperbolic curves

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’ m...

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Bibliographic Details
Main Authors: Leonhardt, Marius (Author) , Lüdtke, Martin (Author) , Müller, Jan Steffen (Author)
Format: Article (Journal)
Language:English
Published: November 2023
In: International mathematics research notices
Year: 2023, Issue: 21, Pages: 18752-18780
ISSN:1687-0247
DOI:10.1093/imrn/rnad185
Online Access:Verlag, kostenfrei, Volltext: https://doi.org/10.1093/imrn/rnad185
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Author Notes:Marius Leonhardt, Martin Lüdtke, and J. Steffen Müller
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Summary: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.
Item Description:Veröffentlicht: 15. August 2023
Gesehen am 23.07.2024
Physical Description:Online Resource
ISSN:1687-0247
DOI:10.1093/imrn/rnad185

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