Cyclicity of finite abelian varieties of type III, submitted. Available here: www2.math.kyushu-u.ac.jp/ virdol
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BibTeX
@MISC{Virdol_cyclicityof,
author = {Cristian Virdol},
title = {Cyclicity of finite abelian varieties of type III, submitted. Available here: www2.math.kyushu-u.ac.jp/ virdol},
year = {}
}
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Abstract
Consider A an abelian variety of dimension r, defined over a number field F, such that EndF A ⊗ Q =EndAF ¯ ⊗ Q, with endomorphism algebra of type I or II in the Albert classification. Assume that A has potential good reduction everywhere. 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 of type I and II, 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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