On a non-abelian analogue of a conjecture of Michael Stoll
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909755547582464 |
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| author | Betts, L. Alexander |
| author_facet | Betts, L. Alexander |
| contents | We formulate a non-abelian generalisation of a conjecture of Stoll, which conjecturally describes the structure of the loci cut out by Kim's method of non-abelian Chabauty. We prove the rank 0 quadratic case of this conjecture, which in particular determines the structure of the quadratic Chabauty locus for once-punctured elliptic curves of rank 0. The proof involves using a variant of the geometric quadratic Chabauty method of Edixhoven and Lido to reduce to an unlikely intersections problem, and ultimately to known results about the relative Manin--Mumford Conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19947 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a non-abelian analogue of a conjecture of Michael Stoll Betts, L. Alexander Number Theory 14G05 (Primary) 11G30, 14H30 (Secondary) We formulate a non-abelian generalisation of a conjecture of Stoll, which conjecturally describes the structure of the loci cut out by Kim's method of non-abelian Chabauty. We prove the rank 0 quadratic case of this conjecture, which in particular determines the structure of the quadratic Chabauty locus for once-punctured elliptic curves of rank 0. The proof involves using a variant of the geometric quadratic Chabauty method of Edixhoven and Lido to reduce to an unlikely intersections problem, and ultimately to known results about the relative Manin--Mumford Conjecture. |
| title | On a non-abelian analogue of a conjecture of Michael Stoll |
| topic | Number Theory 14G05 (Primary) 11G30, 14H30 (Secondary) |
| url | https://arxiv.org/abs/2508.19947 |