Images of ℓ-adic representations and automorphisms of abelian varieties

1996/03/01 by Silverberg, A., Zarhin, Yu. G.
#14K15 (Primary) 11G10 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9603001

Abstract

Suppose F is either a global field or a finitely generated extension of \mathbf Q, A is an abelian variety over F, and ℓ is a prime not equal to the characteristic of F. Let Z denote the center of the endomorphism algebra of A. Let G denote the group of \mathbf Q_ℓ-points of the identity connected component of the Zariski closure of the image of the ℓ-adic representation associated to A. We prove the ℓ-independence of the intersection of G with the torsion subgroup of Z. Our results provide evidence in the direction of the Mumford-Tate Conjecture.

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