Cyclic components of abelian varieties ([formula omitted

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 2r−1 cyclic components.