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 |
|---|---|
| Journal | Journal of Number Theory |
| DOIs | |
| Publication status | Accepted/In press - 2018 Jan 1 |
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All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
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Cyclic components of quotients of abelian varieties mod p. / Virdol, Cristian.
In: Journal of Number Theory, 01.01.2018.Research output: Contribution to journal › Article
TY - JOUR
T1 - Cyclic components of quotients of abelian varieties mod p
AU - Virdol, Cristian
PY - 2018/1/1
Y1 - 2018/1/1
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.
UR - http://www.scopus.com/inward/record.url?scp=85053675309&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85053675309&partnerID=8YFLogxK
U2 - 10.1016/j.jnt.2018.08.005
DO - 10.1016/j.jnt.2018.08.005
M3 - Article
AN - SCOPUS:85053675309
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
ER -