Cyclicity of finite abelian varieties (2012)
by
Cristian Virdol
BibTeX
@MISC{Virdol12cyclicityof,
author = {Cristian Virdol},
title = {Cyclicity of finite abelian varieties},
year = {2012}
}
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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 Ā be the reduction of A at ℘. In this paper, under GRH, for a large family of abelian varieties A, we obtain an asymptotic formula for the number of primes ℘ of F, with NF/Q ℘ ≤ x, for which Ā(F℘) has at most 2r − 1 cyclic components.
Citations
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| 10 | Cyclicity of elliptic curves modulo p and elliptic curve analogues of Linnik’s problem - Cojocaru, Murty |
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| 1 | Cyclicity of finite CM abelian varieties, submitted. Available here: www2.math.kyushu-u.ac.jp/ virdol - Virdol |
| 1 | Cyclicity of finite abelian varieties of type - Virdol |
| 1 | Cyclicity of finite abelian varieties of type III, submitted. Available here: www2.math.kyushu-u.ac.jp/ virdol - Virdol |
