Affine Chabauty I
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915692143443968 |
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| author | Leonhardt, Marius Lüdtke, Martin |
| author_facet | Leonhardt, Marius Lüdtke, Martin |
| contents | We prove finiteness and give an explicit upper bound on the number of $S$-integral points on affine curves satisfying a certain rank-genus inequality. We achieve this by developing an analogue of the Chabauty method, embedding the curve into its generalised Jacobian and bounding the Abel-Jacobi image of the $S$-integral points using arithmetic intersection theory. Our results also provide the foundations for a computational method to determine the set of $S$-integral points on affine curves which will be presented in a follow-up article. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_15949 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Affine Chabauty I Leonhardt, Marius Lüdtke, Martin Number Theory 14G05 (Primary) 11G30, 11S80, 14G40 (Secondary) We prove finiteness and give an explicit upper bound on the number of $S$-integral points on affine curves satisfying a certain rank-genus inequality. We achieve this by developing an analogue of the Chabauty method, embedding the curve into its generalised Jacobian and bounding the Abel-Jacobi image of the $S$-integral points using arithmetic intersection theory. Our results also provide the foundations for a computational method to determine the set of $S$-integral points on affine curves which will be presented in a follow-up article. |
| title | Affine Chabauty I |
| topic | Number Theory 14G05 (Primary) 11G30, 11S80, 14G40 (Secondary) |
| url | https://arxiv.org/abs/2511.15949 |