# Cyclic components of quotients of abelian varieties mod p

Cristian Virdol

Research output: Contribution to journalArticlepeer-review

## Abstract

Let A an abelian variety of dimension r, defined over Q. For p a rational prime, we denote by Fp 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 Γp 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 135-144 10 Journal of Number Theory 197 https://doi.org/10.1016/j.jnt.2018.08.005 Published - 2019 Apr

## All Science Journal Classification (ASJC) codes

• Algebra and Number Theory