Abstract
The aim of this note is to give a simplified proof of the surjectivity of the natural Milnor-Chow homomorphism rho : K-n(M)(A) -> CHn(A,n) between Milnor K-theory and higher Chow groups for essentially smooth (semi-)local k-algebras A with infinite residue fields. It implies the exactness of the Gersten resolution for Milnor K-theory at the generic point. Our method uses the Bloch-Levine moving ...
Abstract
The aim of this note is to give a simplified proof of the surjectivity of the natural Milnor-Chow homomorphism rho : K-n(M)(A) -> CHn(A,n) between Milnor K-theory and higher Chow groups for essentially smooth (semi-)local k-algebras A with infinite residue fields. It implies the exactness of the Gersten resolution for Milnor K-theory at the generic point. Our method uses the Bloch-Levine moving technique and some properties of the Milnor K-theory norm for fields. Furthermore we give new applications.
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