Jean-Morlet Chair - Doctoral school : Frobenius distribution on curves / Chaire Jean-Morlet - Ecole doctorale : distribution de Frobenius sur des courbes

Collection Jean-Morlet Chair - Doctoral school : Frobenius distribution on curves / Chaire Jean-Morlet - Ecole doctorale : distribution de Frobenius sur des courbes

Organizer(s) Kohel, David ; Ritzenthaler, Christophe ; Shparlinski, Igor

Date(s) 17/02/2014 - 28/02/2014

linked URL http://shparlinskikohel.weebly.com/schedule-week-2.html

00:00:00 / 00:00:00

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Distributions des valeurs propres des Frobenius des variétés abéliennes sur un corps fini donné

By Jean-Pierre Serre

Also appears in collections : Abel Prize, The Fields Medallists, Fields medallists - 1954

Soit $k$ un corps fini à $q$ éléments. On s'intéresse aux Frobenius des variétés abéliennes sur $k$ de dimension tendant vers l'infini. Chacune donne une mesure discrète sur le segment $I=\left [ -2\sqrt{q},2\sqrt{q} \right ]$. On désire décrire les mesures sur $I$ qui sont des limites de celles-là. On verra qu'une telle mesure se décompose en somme d'une partie discrète évidente et d'une partie continue non évidente (son support peut être, par exemple, un ensemble de Cantor). Ingrédients: la notion de capacité logarithmique et les résultats de R.M. Robinson sur les entiers algébriques totalement réels.

Information about the video

Date of recording 25/02/2014
Date of publication 20/10/2014
Institution CIRM
Licence CC BY NC ND
Language French
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.18609803
Cite this video Serre, Jean-Pierre (25/02/2014). Distributions des valeurs propres des Frobenius des variétés abéliennes sur un corps fini donné. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.18609803
URL https://dx.doi.org/10.24350/CIRM.V.18609803

Domain(s)

Number Theory

MSC codes

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