Linear and quadratic Chabauty for affine hyperbolic curves

Fuente: arXiv
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Main Authors: Leonhardt, Marius, Lüdtke, Martin, Müller, J. Steffen
Format: Preprint
Published: 2023
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author Leonhardt, Marius
Lüdtke, Martin
Müller, J. Steffen
author_facet Leonhardt, Marius
Lüdtke, Martin
Müller, J. Steffen
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2301_11193
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Linear and quadratic Chabauty for affine hyperbolic curves
Leonhardt, Marius
Lüdtke, Martin
Müller, J. Steffen
Number Theory
14G05 (Primary) 11G30, 11D45 (Secondary)
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.
title Linear and quadratic Chabauty for affine hyperbolic curves
topic Number Theory
14G05 (Primary) 11G30, 11D45 (Secondary)
url https://arxiv.org/abs/2301.11193