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**1 - 1**of**1**### Cyclicity of finite abelian varieties

, 2012

"... Consider A an abelian variety of dimension r, defined over a number field F. For ℘ a finite prime of F, we denote by F ℘ the residue field at ℘. If A has good reduction at ℘, let Ā be the reduction of A at ℘. In this paper, under GRH, for a large family of abelian varieties A, we obtain an asymptoti ..."

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Consider A an abelian variety of dimension r, defined over a number field F. For ℘ a finite prime of F, we denote by F ℘ the residue field at ℘. If A has good reduction at ℘, let Ā be the reduction of A at ℘. In this paper, under GRH, for a large family of abelian varieties A, we obtain an asymptotic formula for the number of primes ℘ of F, with NF/Q ℘ ≤ x, for which Ā(F℘) has at most 2r − 1 cyclic components.