Entanglement in the family of division fields of elliptic curves with complex multiplication
Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
For every CM elliptic curve $E$ defined over a number field $F$ containing the CM field $K$, we prove that the family of $p^{\infty}$-division fields of $E$, with $p \in \mathbb{N}$ prime, becomes linearly disjoint over $F$ after removing an explicit finite subfamily of fields. If $F = K$ and $E$ is obtained as the base-change of an elliptic curve defined over $\mathbb{Q}$, we prove that this finite subfamily is never linearly disjoint over $K$ as soon as it contains more than one element.
Originalsprog | Engelsk |
---|---|
Tidsskrift | Pacific Journal of Mathematics |
Vol/bind | 317 |
Udgave nummer | 1 |
Sider (fra-til) | 21-66 |
ISSN | 0030-8730 |
DOI | |
Status | Udgivet - 2022 |
- math.NT, Primary: 11G05, 14K22, 11G15, Secondary: 11S15, 11F80
Forskningsområder
Links
- https://arxiv.org/pdf/2006.00883.pdf
Accepteret manuskript
ID: 311727485