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

4 18

Brauer-Siegel theorem and analogues for varieties over global fields

The classical Brauer-Siegel theorem can be seen as one of the first instances of description of asymptotical arithmetic: it states that, for a family of number fields $K_i$, under mild conditions (e.g. bounded degree), the product of the regulator by the class number behaves asymptotically like the square root of the discriminant. This can be reformulated as saying that the Brauer-Siegel ratio log($hR$)/ log$\sqrt{D}$ has limit 1. Even if some of the fundamental problems like the existence or non-existence of Siegel zeroes remains unsolved, several generalisations and analog have been developed: Tsfasman-Vladuts, Kunyavskii-Tsfasman, Lebacque-Zykin, Hindry-Pacheco and lately Griffon. These analogues deal with number fields for which the limit is different from 1 or with elliptic curves and abelian varieties either for a fixed variety and varying field or over a fixed field with a family of varieties.

Information about the video

Date of recording 20/06/2017
Date of publication 29/06/2017
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19186103
Cite this video Hindry, Marc (20/06/2017). Brauer-Siegel theorem and analogues for varieties over global fields. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19186103
URL https://dx.doi.org/10.24350/CIRM.V.19186103

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