### Abstract

Let A an abelian variety of dimension r, defined over Q. For p a rational prime, we denote by F_{p} the finite field of cardinality p. If A has good reduction at p, let A¯_{p} be the reduction of A at p. Let Γ be a free subgroup of the Mordell–Weil group A(Q), and let Γ_{p} be the reduction of Γ at p. In this paper for abelian varieties of type I, II, III, and IV, under Generalized Riemann Hypothesis, Artin's Holomorphy Conjecture, and Pair Correlation Conjecture, we obtain asymptotic formulas for the number of primes p, with p≤x, for which the quotient [Formula presented] has at most 2r−1 cyclic components.

Original language | English |
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Pages (from-to) | 135-144 |

Number of pages | 10 |

Journal | Journal of Number Theory |

Volume | 197 |

DOIs | |

Publication status | Published - 2019 Apr |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

Virdol, C. (2019). Cyclic components of quotients of abelian varieties mod p.

*Journal of Number Theory*,*197*, 135-144. https://doi.org/10.1016/j.jnt.2018.08.005