As pointed out in [Reference Gaudron and RémondGR17, § 3], Lemma 6 of [Reference SilverbergSil88] is false as stated. Thus, the proofs of the results that rely on it are not correct as stated. These include the proofs of [Reference SilverbergSil88, Corollaries 4–8], the proofs of [Reference SilverbergSil92, Corollaries 5.2(i), 5.3(i), and 5.4(i,ii)], and the proofs of the results in [Reference van MulbregtvMu92] for non-simple two- and three-dimensional abelian varieties. The proof given in [Reference SilverbergSil88, Lemma 6] is valid with the additional assumption that the abelian variety $A$ is (absolutely) simple. Even without that assumption, the proofs of the corollaries can be salvaged in certain cases; however, stronger results have recently been achieved in [Reference Gaudron and RémondGR17].
I thank Gaël Rémond and Éric Gaudron for pointing out this error.