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

13 18

Survey on quaternion hermitian lattices and its application to supersingular abelian varieties

By Tomoyoshi Ibukiyama

The theme of the survey is how arithmetic theory of quatenion hermitian lattices can be applied to the theory of supersingular abelian varieties. Here the following geometric objects will be explained by arithmetics. Principal polarizations of superspecial abelian varieties, of supersingular surfaces, components of supersingular moduli and their configuration for small dimensions, their automorphims, fields of definition, and existence of maximal curves of genus three over $F_{p}^{2}$ for all odd primes $p$. Corresponding arithmetics are class numbers, type numbers, lattice automorphisms, and parahoric subgroups of quaternion hermitian groups, mass or trace formulas.

Information about the video

Date of recording 01/06/2021
Date of publication 13/07/2021
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers
Director(s) Guillaume Hennenfent
Format MP4

Citation data

DOI 10.24350/CIRM.V.19760703
Cite this video Ibukiyama, Tomoyoshi (01/06/2021). Survey on quaternion hermitian lattices and its application to supersingular abelian varieties. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19760703
URL https://dx.doi.org/10.24350/CIRM.V.19760703

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