The abelian part of a compatible system and l-independence of the Tate conjecture

Let K be a number field and {V-l}(l) a rational strictly compatible system of semisimple Galois representations of K arising from geometry. Let G(l) and V-l(ab) be respectively the algebraic monodromy group and the maximal abelian subrepresentation of V-l for all l. We prove that the system {V-l(ab)}(l) is also a rational strictly compatible system under some group theoretic conditions, e.g., when G(l)' is connected and satisfies Hypothesis A for some prime l'. As an application, we prove that the Tate conjecture for abelian variety X/K is independent of l if the algebraic monodromy groups of the Galois representations of X satisfy the required conditions.