Article ID Journal Published Year Pages File Type
4593462 Journal of Number Theory 2016 8 Pages PDF
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℘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℘≤xNF/Q℘≤x, for which A¯(F℘) has at most 2r−12r−1 cyclic components.

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Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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