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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2501.18541 |
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| _version_ | 1866908402990448640 |
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| author | Guo, Haoyang Yang, Ziquan |
| author_facet | Guo, Haoyang Yang, Ziquan |
| contents | In this article, we aim to largely complete the program of proving the Tate conjecture for surfaces of geometric genus one, by introducing techniques to analyze those surfaces whose "natural models" are singular. As an application, we show that every elliptic curve of height one over a global function field of genus one and characteristic $p \ge 11$ satisfies the Birch--Swinnerton-Dyer conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18541 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Tate conjecture for surfaces of geometric genus one -- embracing singularities Guo, Haoyang Yang, Ziquan Algebraic Geometry In this article, we aim to largely complete the program of proving the Tate conjecture for surfaces of geometric genus one, by introducing techniques to analyze those surfaces whose "natural models" are singular. As an application, we show that every elliptic curve of height one over a global function field of genus one and characteristic $p \ge 11$ satisfies the Birch--Swinnerton-Dyer conjecture. |
| title | The Tate conjecture for surfaces of geometric genus one -- embracing singularities |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2501.18541 |