Milnor K-theory of smooth quasiprojective varieties

Let k be a field. Among the algebraic invariants associated to k are the Milnor Kgroups, one for each integer n ≥ 0. These abelian groups were first defined (but not so named) by Milnor in the context of quadratic forms [Mi]. The definition is completely algebraic; nevertheless, a beautiful geometric connection with Bloch’s higher Chow groups was discovered by Nesterenko-Suslin [NS] and Totaro [To]; specifically, that there is a natural map inducing an isomorphism