Abstract
We identify the Milnor K-theory of a field with a certain higher Chow group. One of the important consequences of Grothendieck's Riemann-Roch theorem is that Ko(X) ® Q ~ (~ CH'(X) ® Q, p for any smooth algebraic variety X. Here Ko(X) is the Grothendieck group of vector bundles on X, and CHP(X) is the Chow group of codimension-p algebraic cycles on X. Recently, Bloch (23 has shown that Quillen's higher algebraic K-theory of X has a similar decomposition. He defines groups CHP(X, n) in terms of certain codimen- sion-p algebraic cycles on X × A', and we have
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