 Using the theory of motives, it is possible to refine the weight filtration on the cohomology with rational coefficients to one with integral coefficients.The machinery based on the notions of Hodge structure and mixed Hodge structure forms a part of still largely conjectural theory of motives envisaged by Alexander Grothendieck.Arithmetic information for nonsingular algebraic variety "X", encoded by eigenvalue of Frobenius elements acting on its l-adic cohomology, has something in common with the Hodge structure arising from "X" considered as a complex algebraic variety.