Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.23381 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915644116566016 |
|---|---|
| author | Allen, Sam Genao, Tyler |
| author_facet | Allen, Sam Genao, Tyler |
| contents | In this paper, we prove that for each number field $F$ there exists a uniform bound on the prime levels $p$ of elliptic curves $E/F$ for which $F(E[p])=F(ζ_p)$. Under the Generalized Riemann Hypothesis, we also give uniform bounds on $p$ for which $F(E[p])/F$ is abelian, provided that $F$ has no rational complex multiplication. These are generalizations of results of González-Jiménez and Lozano-Robledo to general number fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23381 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform bounds on the level of cyclotomic division fields of elliptic curves Allen, Sam Genao, Tyler Number Theory 11G05 In this paper, we prove that for each number field $F$ there exists a uniform bound on the prime levels $p$ of elliptic curves $E/F$ for which $F(E[p])=F(ζ_p)$. Under the Generalized Riemann Hypothesis, we also give uniform bounds on $p$ for which $F(E[p])/F$ is abelian, provided that $F$ has no rational complex multiplication. These are generalizations of results of González-Jiménez and Lozano-Robledo to general number fields. |
| title | Uniform bounds on the level of cyclotomic division fields of elliptic curves |
| topic | Number Theory 11G05 |
| url | https://arxiv.org/abs/2511.23381 |