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

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

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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.

Reference: https://arxiv.org/abs/1806.10842

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