Graph isomorphism conjecture for Milnor K-theory and higher Chow groups

Let $k$) be a field with sufficiently large cardinality, and let $A$ be a semi-local $k$-algebra essentially of finite type. The graph homomorphism

$$g r_A: K_n^M(A)\longrightarrow \mathbf{C}\mathbf{H}^n(A,n)$$

Graph isomorphism conjecture. For every such $A$, the graph homomorphism is an isomorphism.

This conjecture predicts that, over fields of sufficiently large cardinality, Milnor $K$-theory of semi-local algebras is completely captured by the corresponding higher Chow groups. Its resolution is not indicated in the supplied text.