K3 surfaces over number fields and $l$-adic representations

The Tate conjecture on algebraic cycles is proved for any algebraic K3 surface over a number field. If the canonical representation of the Hodge group in the $\mathbf Q$-lattice of transcendental cohomology classes is absolutely irreducible, then the Mumford–Tate conjecture is true for such a K3 surface.
Bibliography: 18 titles.