Comparison of component groups of -adic and mod monodromy groups

Let \_{: GalKₙ (Q_) \}_ be a semisimple compatible system of -adic representations of a number field K that is arising from geometry. Let G_₍, ₐ_ and G_{}₍, ₅_ be respectively the algebraic monodromy group and full algebraic envelope of _. We prove that there is a natural isomorphism between the component groups ₀ (G_) ₀ (G_) for all sufficiently large.