 The Bernstein filtration not being available on "D""X" for general varieties "X", the definition is generalized to arbitrary affine smooth varieties "X" by means of "order filtration" on "D""X", defined by the order of differential operators.The associated graded ring gr "D""X" is given by regular functions on the cotangent bundle T∗"X".The "characteristic variety" is defined to be the subvariety of the cotangent bundle cut out by the radical of the annihilator of gr "M", where again "M" is equipped with a suitable filtration (with respect to the order filtration on "D""X").