Buchumschlag

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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Hauptverfasser: Leonhardt, Marius (Verfasst von) , Lüdtke, Martin (Verfasst von) , Müller, Jan Steffen (Verfasst von)
Dokumenttyp: Article (Journal)
Sprache:Englisch
Veröffentlicht: November 2023
In: International mathematics research notices
Year: 2023, Heft: 21, Pages: 18752-18780
ISSN:1687-0247
DOI:10.1093/imrn/rnad185
Online-Zugang:Verlag, kostenfrei, Volltext: https://doi.org/10.1093/imrn/rnad185
Volltext
Verfasserangaben:Marius Leonhardt, Martin Lüdtke, and J. Steffen Müller
Beschreibung
Zusammenfassung: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.
Beschreibung:Veröffentlicht: 15. August 2023
Gesehen am 23.07.2024
Beschreibung:Online Resource
ISSN:1687-0247
DOI:10.1093/imrn/rnad185

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