### 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 |

### All Science Journal Classification (ASJC) codes

- Algebra and Number Theory

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## Cite this

Virdol, C. (2016). Cyclic components of abelian varieties (mod).

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