inspired in part by matsumoto's theorem, milnor made a definition of the higher "k"-groups of a field. he referred to his definition as "purely "ad hoc"", and it neither appeared to generalize to all rings nor did it appear to be the correct definition of the higher "k"-theory of fields. much later, it was discovered by nesterenko and suslin and by totaro that milnor "k"-theory is actually a direct summand of the true "k"-theory of the field. specifically, "k"-groups have a filtration called the "weight filtration", and the milnor "k"-theory of a field is the highest weight-graded piece of the "k"-theory. additionally, thomason discovered that there is no analog of milnor "k"-theory for a general variety.