Cyclicity of the rational points group of abelian varieties over finite fields

Alejandro Giangreco
I2M, Aix-Marseille Université

Date(s) : 16/10/2018   iCal
10 h 06 min - 11 h 06 min

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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