The integral Hasse principle for stacky curves associated to a family of generalized Fermat equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908701063905280 |
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| author | Duque-Rosero, Juanita Keyes, Christopher Kobin, Andrew Roy, Manami Sankar, Soumya Wang, Yidi |
| author_facet | Duque-Rosero, Juanita Keyes, Christopher Kobin, Andrew Roy, Manami Sankar, Soumya Wang, Yidi |
| contents | We characterize the integral Hasse principle for an infinite family of spherical stacky curves with genus $g\in [2/3,1)$ that are defined using generalized Fermat equations, extending a result of Darmon and Granville. We then apply our methods to find that a positive proportion of curves in our family satisfy the integral Hasse principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_13248 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The integral Hasse principle for stacky curves associated to a family of generalized Fermat equations Duque-Rosero, Juanita Keyes, Christopher Kobin, Andrew Roy, Manami Sankar, Soumya Wang, Yidi Number Theory Algebraic Geometry Primary 11D45, 14G12, 14D23, Secondary 11D41, 14G05, 14Q25 We characterize the integral Hasse principle for an infinite family of spherical stacky curves with genus $g\in [2/3,1)$ that are defined using generalized Fermat equations, extending a result of Darmon and Granville. We then apply our methods to find that a positive proportion of curves in our family satisfy the integral Hasse principle. |
| title | The integral Hasse principle for stacky curves associated to a family of generalized Fermat equations |
| topic | Number Theory Algebraic Geometry Primary 11D45, 14G12, 14D23, Secondary 11D41, 14G05, 14Q25 |
| url | https://arxiv.org/abs/2509.13248 |