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H 1 Good recursive towers

Auteurs : Bassa, Alp (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Curves over finite fields of large genus with many rational points have been of interest for both theoretical reasons and for applications. In the past, various methods have been employed for the construction of such curves. One such method is by means of explicit recursive equations and will be the emphasis of this talk.The first explicit examples were found by Garcia-Stichtenoth over quadratic finite fields in 1995. Afterwards followed the discovery of good towers over cubic finite fields and finally all nonprime finite fields in 2013 (B.-Beelen-Garcia-Stichtenoth). The recursive nature of these towers makes them very special and in fact all good examples have been shown to have a modular interpretation of some sort. The questions of finding good recursive towers over prime fields resisted all attempts for several decades and lead to the common belief that such towers might not exist. In this talk I will try to give an overview of the landscape of explicit recursive towers and present a recently discovered tower over all finite fields including prime fields, except $F_{2}$ and $F_{3}$.
    This is joint work with Christophe Ritzenthaler.

    Keywords : recursive towers ; curves over finite fields

    Codes MSC :
    11G20 - Curves over finite and local fields
    11T71 - Algebraic coding theory; cryptography
    14G05 - Rational points
    14G15 - Finite ground fields
    14H25 - Arithmetic ground fields, See also {11Dxx,11G05,14Gxx}

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 04/07/2019
      Date de captation : 10/06/2019
      Collection : Research talks
      Format : MP4
      Durée : 01:05:44
      Domaine : Algebraic & Complex Geometry ; Number Theory
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2019-06-10_Bassa.mp4

    Informations sur la rencontre

    Nom de la rencontre : Arithmetic, Geometry, Cryptography and Coding Theory / Arithmétique, géométrie, cryptographie et théorie des codes
    Organisateurs de la rencontre : Ballet, Stéphane ; Bisson, Gaetan ; Bouw, Irene
    Dates : 10/06/2019 - 14/06/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/1921.html

    Citation Data

    DOI : 10.24350/CIRM.V.19537303
    Cite this video as: Bassa, Alp (2019). Good recursive towers. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19537303
    URI : http://dx.doi.org/10.24350/CIRM.V.19537303


    Voir aussi

    Bibliographie

    1. Bassa, A., & Ritzenthaler, C. (2018). Good recursive towers over prime fields exist. arXiv preprint arXiv:1807.05714 - https://arxiv.org/abs/1807.05714

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