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H 1 Monogenic cubic fields and local obstructions

Auteurs : Shnidman, Ari (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : A number field is monogenic if its ring of integers is generated by a single element. It is conjectured that for any degree d > 2, the proportion of degree d number fields which are monogenic is 0. There are local obstructions that force this proportion to be < 100%, but beyond this very little is known. I’ll discuss work with Alpoge and Bhargava showing that a positive proportion of cubic fields (d = 3) have no local obstructions and yet are still not monogenic. This uses new results on ranks of Selmer groups of elliptic curves in twist families.

    Keywords : cubic fields; elliptic curves

    Codes MSC :
    11G05 - Elliptic curves over global fields
    11R16 - Cubic and quartic extensions

      Informations sur la Vidéo

      Réalisateur : Hennenfent, Guillaume
      Langue : Anglais
      Date de publication : 20/12/2019
      Date de captation : 05/12/2019
      Collection : Research talks ; Number Theory
      Format : MP4
      Durée : 00:54:21
      Domaine : Number Theory
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-12-05_Shnidman.mp4

    Informations sur la rencontre

    Nom de la rencontre : Zeta Functions / Fonctions Zêta
    Organisateurs de la rencontre : Armana, Cécile ; Fiorilli, Daniel ; Jouve, Florent ; Louboutin, Stephane
    Dates : 02/12/2019 - 06/12/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/2062.html

    Citation Data

    DOI : 10.24350/CIRM.V.19586203
    Cite this video as: Shnidman, Ari (2019). Monogenic cubic fields and local obstructions. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19586203
    URI : http://dx.doi.org/10.24350/CIRM.V.19586203

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