Entanglement in the family of division fields of elliptic curves with complex multiplication
Research output: Contribution to journal › Journal article › Research › peer-review
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.
Original language | English |
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Journal | Pacific Journal of Mathematics |
Volume | 317 |
Issue number | 1 |
Pages (from-to) | 21-66 |
ISSN | 0030-8730 |
DOIs | |
Publication status | Published - 2022 |
Bibliographical note
32 pages. This revision fixes minor issues, updates the references and includes new results (Corollary 4.6 and Theorem 4.9). Comments are more than welcome!
- Elliptic curves, Complex Multiplication, Entanglement, Division fields
Research areas
Links
- https://arxiv.org/pdf/2006.00883.pdf
Accepted author manuscript
ID: 311727485