The automorphism group of the $p^{n}$-torsion points of an elliptic curve over a field of characteristic $p \ge 5$
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912074332897280 |
|---|---|
| author | Im, Bo-Hae Kim, Hansol |
| author_facet | Im, Bo-Hae Kim, Hansol |
| contents | For a field $K$ of characteristic $p\ge5$ and the elliptic curve $E_{s,t}: y^{2} = x^{3} + sx + t$ defined over the function field $K\left(s,t\right)$ of two variables $s$ and $t$, we prove that for a positive integer $n$, the automorphism group of the normal extension $K\left(s,t\right)\left(E_{s,t}\left[p^{n}\right]\right)/K\left(s,t\right)$ is isomorphic to $\left(\mathbb{Z}/p^{n}\mathbb{Z}\right)^{\times}$, and its inseparable degree is $p^{n}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11353 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The automorphism group of the $p^{n}$-torsion points of an elliptic curve over a field of characteristic $p \ge 5$ Im, Bo-Hae Kim, Hansol Number Theory For a field $K$ of characteristic $p\ge5$ and the elliptic curve $E_{s,t}: y^{2} = x^{3} + sx + t$ defined over the function field $K\left(s,t\right)$ of two variables $s$ and $t$, we prove that for a positive integer $n$, the automorphism group of the normal extension $K\left(s,t\right)\left(E_{s,t}\left[p^{n}\right]\right)/K\left(s,t\right)$ is isomorphic to $\left(\mathbb{Z}/p^{n}\mathbb{Z}\right)^{\times}$, and its inseparable degree is $p^{n}$. |
| title | The automorphism group of the $p^{n}$-torsion points of an elliptic curve over a field of characteristic $p \ge 5$ |
| topic | Number Theory |
| url | https://arxiv.org/abs/2410.11353 |