Equivalence of conjectures on heavenly elliptic curves
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909704282701824 |
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| author | McLeman, Cam Rasmussen, Christopher |
| author_facet | McLeman, Cam Rasmussen, Christopher |
| contents | Heavenly abelian varieties are abelian varieties defined over number fields that exhibit constrained $\ell$-adic Galois representations for some rational prime $\ell$. At the ICMS Workshop held in November 2024, we presented evidence for two finiteness conjectures around the distribution of heavenly elliptic curves over quadratic number fields, one in terms of isomorphism classes of curves, and a second in terms of quadratic fields which admit heavenly elliptic curves. We prove these two conjectures are equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17474 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equivalence of conjectures on heavenly elliptic curves McLeman, Cam Rasmussen, Christopher Number Theory 11G05 Heavenly abelian varieties are abelian varieties defined over number fields that exhibit constrained $\ell$-adic Galois representations for some rational prime $\ell$. At the ICMS Workshop held in November 2024, we presented evidence for two finiteness conjectures around the distribution of heavenly elliptic curves over quadratic number fields, one in terms of isomorphism classes of curves, and a second in terms of quadratic fields which admit heavenly elliptic curves. We prove these two conjectures are equivalent. |
| title | Equivalence of conjectures on heavenly elliptic curves |
| topic | Number Theory 11G05 |
| url | https://arxiv.org/abs/2505.17474 |