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Quadratic twist families of elliptic curves with unusual $2^{\infty }$-Selmer groups
Multi angle
Authors : Smith, Alexander (Author of the conference)
CIRM (Publisher )
11G20 - Curves over finite and local fields
CIRM (Publisher )
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Abstract :
Given any elliptic curve $E$ over the rationals, we show that 50 % of the quadratic twists of $E$ have $2^{\infty}$-Selmer corank 0 and 50 % have $2^{\infty}$-Selmer corank 1. As a result, we show that Goldfeld's conjecture follows from the Birch and Swinnerton-Dyer conjecture.
MSC Codes : 11G20 - Curves over finite and local fields
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 30/05/2023 Conference Date : 16/05/2023 Subseries : Research talks arXiv category : Number Theory Mathematical Area(s) : Number Theory Format : MP4 (.mp4) - HD Video Time : 00:59:52 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-05-16_Smith.mp4 
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Information on the Event
Event Title : Jean-Morlet Chair - Conference - Arithmetic Statistics / Chaire Jean-Morlet - Conférence - Statistiques arithmétiquesEvent Organizers : Anni, Samuele ; Stevenhagen, Peter ; Vonk, Jan ; Lorenzo Garcia, Elisa Dates : 15/05/2023 - 19/05/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2675.html
Citation Data
DOI : 10.24350/CIRM.V.20046203Cite this video as: Smith, Alexander (2023). Quadratic twist families of elliptic curves with unusual $2^{\infty }$-Selmer groups. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20046203 URI : http://dx.doi.org/10.24350/CIRM.V.20046203 |
See Also
- [Multi angle] Integers expressible as the sum of two rational cubes / Author of the conference Bhargava, Manjul.
- [Multi angle] The average size of 3-torsion in class groups of 2-extensions / Author of the conference Matchett Wood, Melanie.
- [Multi angle] On arithmetic statistics / Author of the conference Stevenhagen, Peter.
- [Multi angle] Subrings of number fields / Author of the conference Lenstra, Hendrik.
- [Multi angle] Vanishing of twisted L-functions of elliptic curves over function fields / Author of the conference Lalin, Matilde.
Bibliography
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