 Deligne has proved that the "n"th cohomology group of an arbitrary algebraic variety has a canonical mixed Hodge structure.This structure is functorial, and compatible with the products of varieties ("Künneth isomorphism") and the product in cohomology.For a complete nonsingular variety "X" this structure is pure of weight "n", and the Hodge filtration can be defined through the hypercohomology of the truncated de Rham complex.