Quadratic twist families of elliptic curves with unusual $2^{\infty }$-Selmer groups

Appears in collection : Jean-Morlet Chair - Conference - Arithmetic Statistics / Chaire Jean-Morlet - Conférence - Statistiques arithmétiques

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.

Information about the video

Date of recording 16/05/2023
Date of publication 30/05/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.20046203
Cite this video Smith, Alexander (16/05/2023). Quadratic twist families of elliptic curves with unusual $2^{\infty }$-Selmer groups. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.20046203
URL https://dx.doi.org/10.24350/CIRM.V.20046203