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Asymptotic distribution of Frobenius roots for curves and abelian varieties over a finite field
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Authors : Tsfasman, Michael (Author of the conference)
CIRM (Publisher )
11R04 - Algebraic numbers; rings of algebraic integers
11R58 - Arithmetic theory of algebraic function fields
11S40 - Zeta functions and $L$-functions
14G15 - Finite ground fields
14K15 - Arithmetic ground fields
CIRM (Publisher )
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Abstract :
We are interested in the behaviour of Frobenius roots when the base field is fixed and the genus of the curve or the dimension of the abelian variety tends to infinity. I shall explain how to put the question and what are the answers. This happens to be a question in algebraic number theory and harmonic analysis. For curves (and for number fields) these are my old results with Serge Vladuts, for abelian varieties those of J.-P. Serre (séminaire Bourbaki, 2018) and my work in progress with Nicolas Nadirashvili.
Keywords : Frobenius roots; algebraic numbers; abelian varieties; measure; potential
MSC Codes : Keywords : Frobenius roots; algebraic numbers; abelian varieties; measure; potential
11R04 - Algebraic numbers; rings of algebraic integers
11R58 - Arithmetic theory of algebraic function fields
11S40 - Zeta functions and $L$-functions
14G15 - Finite ground fields
14K15 - Arithmetic ground fields
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 06/03/2023 Conference Date : 16/02/2023 Subseries : Research talks arXiv category : Algebraic Geometry ; Number Theory ; Analysis of PDEs Mathematical Area(s) : Analysis and its Applications ; Algebraic & Complex Geometry ; Number Theory Format : MP4 (.mp4) - HD Video Time : 01:04:31 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-02-16_Tsfasman.mp4 
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Information on the Event
Event Title : COGNACEvent Organizers : Aubry, Yves ; Ballet, Stéphane ; Cardinali, Ilaria ; Gorla, Elisa Dates : 13/02/2023 - 17/02/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2803.html
Citation Data
DOI : 10.24350/CIRM.V.20001903Cite this video as: Tsfasman, Michael (2023). Asymptotic distribution of Frobenius roots for curves and abelian varieties over a finite field. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.20001903 URI : http://dx.doi.org/10.24350/CIRM.V.20001903 |
See Also
- [Multi angle] Factoring polynomials over function fields / Author of the conference Voloch, José Felipe.
- [Multi angle] An overview of algebraic geometry codes from surfaces / Author of the conference Nardi, Jade.
- [Multi angle] Algebraic curves with many rational points over finite fields / Author of the conference Montanucci, Maria.
- [Multi angle] Lower bound on the maximal number of rational points on curves over finite fields / Author of the conference Lorenzo Garcia, Elisa.
Bibliography
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