TY - JOUR

T1 - Cyclic components of quotients of abelian varieties mod p

AU - Virdol, Cristian

N1 - Publisher Copyright:
© 2018 Elsevier Inc.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

PY - 2019/4

Y1 - 2019/4

N2 - 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.

AB - 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.

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U2 - 10.1016/j.jnt.2018.08.005

DO - 10.1016/j.jnt.2018.08.005

M3 - Article

AN - SCOPUS:85053675309

VL - 197

SP - 135

EP - 144

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -