 This action must have the property that a real number "a" acts by "an".The subspace "H""p","q" is the subspace on which formula_24 acts as multiplication by formula_25
In the theory of motives, it becomes important to allow more general coefficients for the cohomology.The definition of a Hodge structure is modified by fixing a Noetherian subring A of the field formula_26 of real numbers, for which formula_27 is a field.