Linear and Quadratic Chabauty for Affine Hyperbolic Curves

Marius Leonhardt; Martin Lüdtke; Steffen Müller

doi:10.1093/imrn/rnad185

Linear and Quadratic Chabauty for Affine Hyperbolic Curves

Marius Leonhardt, Martin Lüdtke^*, Steffen Müller

^*Corresponding author for this work

Algebra

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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 ≤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 language	English
Pages (from-to)	18752–18780
Number of pages	29
Journal	International Mathematics Research Notices
Volume	2023
Issue number	21
Early online date	15-Aug-2023
DOIs	https://doi.org/10.1093/imrn/rnad185
Publication status	Published - Nov-2023

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Linear and Quadratic Chabauty for Affine Hyperbolic Curves Final publisher's version, 669 KBLicence: CC BY

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title = "Linear and Quadratic Chabauty for Affine Hyperbolic Curves",

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 ≤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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year = "2023",

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AU - Lüdtke, Martin

AU - Müller, Steffen

PY - 2023/11

Y1 - 2023/11

N2 - 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.

AB - 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.

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U2 - 10.1093/imrn/rnad185

DO - 10.1093/imrn/rnad185

M3 - Article

SN - 1073-7928

VL - 2023

SP - 18752

EP - 18780

JO - International Mathematics Research Notices

JF - International Mathematics Research Notices

IS - 21

ER -

Linear and Quadratic Chabauty for Affine Hyperbolic Curves

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