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H 1 Good recursive towers

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

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

 Informations sur la Vidéo Langue : Anglais Date de publication : 04/07/2019 Date de captation : 10/06/2019 Collection : Research talks ; Algebraic and Complex Geometry ; Number Theory 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 codesOrganisateurs de la rencontre : Ballet, Stéphane ; Bisson, Gaetan ; Bouw, IreneDates : 10/06/2019 - 14/06/2019 Année de la rencontre : 2019 URL Congrès : https://conferences.cirm-math.fr/1921.htmlCitation 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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