Abstract
For a prime number ℓ, an isogeny class A of abelian varieties is called ℓ-cyclic if every variety in A have a cyclic ℓ-part of its group of rational points. More generally, for a finite set of prime numbers S, A is said to be S-cyclic if it is ℓ-cyclic for every ℓ∈S. We give lower and upper bounds on the fraction of S-cyclic g-dimensional isogeny classes of abelian varieties defined over the finite field Fq, when q tends to infinity.
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