Cyclicity of the rational points group of abelian varieties over finite fields
Alejandro Giangreco
I2M, Aix-Marseille Université
https://sites.google.com/view/alejandro-giangreco/home
Date(s) : 16/10/2018 iCal
10h06 - 11h06
The group of rational points of an abelian variety defined over a finite field is a finite abelian group and it has a theoretical and practical interest, for example in cryptography, where the discrete logarithm problem can be exploited. In this talk I give some statistical results on the fraction of « cyclic isogeny classes » of abelian varieties (i.e. those isogeny classes where all the varieties have a cyclic group of rational points). With this purpose I start by giving some criteria to know if an abelian variety is « cyclic », i.e. it has a cyclic group of rational points.
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Reference: https://arxiv.org/abs/1806.10842
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