Linear and quadratic Chabauty for affine hyperbolic curves
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914964835401728 |
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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 |