Elliptic surfaces to class groups and Selmer groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909762862448640 |
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| author | Banerjee, Kalyan Chakraborty, Kalyan Hoque, Azizul |
| author_facet | Banerjee, Kalyan Chakraborty, Kalyan Hoque, Azizul |
| contents | In this note, we connect the $n$-torsions of the Picard group of an elliptic surface to the $n$-divisibility of the class group of torsion fields for a given integer $n>1$. We also connect the $n$-divisibility of the Selmer group to that of the class group of torsion fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00551 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elliptic surfaces to class groups and Selmer groups Banerjee, Kalyan Chakraborty, Kalyan Hoque, Azizul Number Theory Algebraic Geometry In this note, we connect the $n$-torsions of the Picard group of an elliptic surface to the $n$-divisibility of the class group of torsion fields for a given integer $n>1$. We also connect the $n$-divisibility of the Selmer group to that of the class group of torsion fields. |
| title | Elliptic surfaces to class groups and Selmer groups |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2509.00551 |