### Abstract

Consider A an abelian variety of dimension r, defined over a number field F. For a finite prime of F, we denote by F the residue field at . If A has good reduction at , let A- be the reduction of A at . In this paper, under GRH, we obtain an asymptotic formula for the number of primes of F, with NF/Q≤x, for which A-(F) has at most 2. r- 1 cyclic components.

Original language | English |
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Pages (from-to) | 426-433 |

Number of pages | 8 |

Journal | Journal of Number Theory |

Volume | 159 |

DOIs | |

Publication status | Published - 2016 Feb 1 |

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### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

### Cite this

*Journal of Number Theory*,

*159*, 426-433. https://doi.org/10.1016/j.jnt.2015.08.015

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*Journal of Number Theory*, vol. 159, pp. 426-433. https://doi.org/10.1016/j.jnt.2015.08.015

**Cyclic components of abelian varieties (mod).** / Virdol, Cristian.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Cyclic components of abelian varieties (mod)

AU - Virdol, Cristian

PY - 2016/2/1

Y1 - 2016/2/1

N2 - Consider A an abelian variety of dimension r, defined over a number field F. For a finite prime of F, we denote by F the residue field at . If A has good reduction at , let A- be the reduction of A at . In this paper, under GRH, we obtain an asymptotic formula for the number of primes of F, with NF/Q≤x, for which A-(F) has at most 2. r- 1 cyclic components.

AB - Consider A an abelian variety of dimension r, defined over a number field F. For a finite prime of F, we denote by F the residue field at . If A has good reduction at , let A- be the reduction of A at . In this paper, under GRH, we obtain an asymptotic formula for the number of primes of F, with NF/Q≤x, for which A-(F) has at most 2. r- 1 cyclic components.

UR - http://www.scopus.com/inward/record.url?scp=84944810066&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944810066&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2015.08.015

DO - 10.1016/j.jnt.2015.08.015

M3 - Article

VL - 159

SP - 426

EP - 433

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -