Arithmetic, Geometry, Cryptography and Coding Theory / Arithmétique, géométrie, cryptographie et théorie des codes

Collection Arithmetic, Geometry, Cryptography and Coding Theory / Arithmétique, géométrie, cryptographie et théorie des codes

Organizer(s) Anni, Samuele ; Karemaker, Valentijn ; Lorenzo Garcia, Elisa

Date(s) 31/05/2021 - 04/06/2021

linked URL https://conferences.cirm-math.fr/2558.html

00:00:00 / 00:00:00

1 18

Good recursive towers

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.

Information about the video

Date of recording 10/06/2019
Date of publication 04/07/2019
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19537303
Cite this video Bassa, Alp (10/06/2019). Good recursive towers. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19537303
URL https://dx.doi.org/10.24350/CIRM.V.19537303

Domain(s)

Bibliography

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

MSC codes

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