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Vertical coincidences of an elliptic curve defined over a number field
Multi angle
Authors : Yvon, Zoé (Author of the conference)
CIRM (Publisher )
11F80 - Galois representations
11G05 - Elliptic curves over global fields
11R32 - Galois theory
CIRM (Publisher )
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Abstract :
Let $E/F$ be an elliptic curve over a number field $F$. For a prime $p$, the extension $F(E[p^k])/F$ generated by the coordinates of the $p^k$-torsion points, is finite and Galois. We consider when the coincidence $F(E[p^k])=F(E[p^{k+1}])$ holds. Daniels and Lozano-Robledo classified such coincidences when $F=\mathbb{Q}$. In this talk, we will describe some results over a general number field $F$ and give additional possible coincidencesin this larger case.
Keywords : elliptic curves; Galois representations; entanglement; Galois theory
MSC Codes : Keywords : elliptic curves; Galois representations; entanglement; Galois theory
11F80 - Galois representations
11G05 - Elliptic curves over global fields
11R32 - Galois theory
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 03/07/2025 Conference Date : 09/06/2025 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory ; Algebraic & Complex Geometry Format : MP4 (.mp4) - HD Video Time : 00:28:37 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2025-06-09_Yvon.mp4 
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Information on the Event
Event Title : AGCT 2025 - Arithmetic, Geometry, Cryptography and Coding Theory / AGCT 2025 - Arithmétique, Géométrie, Cryptographie et Théorie des CodesEvent Organizers : Aubry, Yves ; Pazuki, Fabien ; Salgado, Cecilia Dates : 09/06/2025 - 13/06/2025 Event Year : 2025 Event URL : https://conferences.cirm-math.fr/3343.html
Citation Data
DOI : 10.24350/CIRM.V.20363703Cite this video as: Yvon, Zoé (2025). Vertical coincidences of an elliptic curve defined over a number field. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20363703 URI : http://dx.doi.org/10.24350/CIRM.V.20363703 |
See Also
- [Multi angle] Reducing models for branched covers of the projective line / Author of the conference Voight, John.
- [Multi angle] Structure of supersingular elliptic curve isogeny graphs / Author of the conference Scheidler, Renate.
- [Multi angle] Automorphism groups of algebraic curves in positive characteristic / Author of the conference Montanucci, Maria.
- [Multi angle] The point-hyperplane geometry: relatively universal embeddings and associated codes / Author of the conference Cardinali, Ilaria.
- [Multi angle] Evaluation codes in the sum-rank metric / Author of the conference Berardini, Elena.
Bibliography
- DANIELS, Harris B. et LOZANO-ROBLEDO, Álvaro. Coincidences of division fields. , Annales de l'Institut Fourier. 2023. p. 163-202. - https://doi.org/10.5802/aif.3520
- GONZÁLEZ–JIMÉNEZ, Enrique et LOZANO-ROBLEDO, Álvaro. Elliptic curves with abelian division fields. Mathematische Zeitschrift, 2016, vol. 283, p. 835-859. - https://doi.org/10.1007/s00209-016-1623-z
- ROUSE, Jeremy et ZUREICK-BROWN, David. Elliptic curves over ℚ and 2-adic images of Galois. Research in Number Theory, 2015, vol. 1, no 1, p. 12. - https://doi.org/10.1007/s40993-015-0013-7
- SERRE, Jean-Pierre. Propriétés galoisiennes des points d'ordre fini des courbes elliptiques. Invent. math, 1971, vol. 15, p. 259-331. - https://doi.org/10.1007/BF01405086
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