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The Milnor-Chow homomorphism revisited

Moritz Kerz, Stefan Müller-Stach

Number 17
Author Stefan Müller-Stach
Year 2007
Journal K-Theory (Springer Verlag) vol. 38 (1), 49-58 (2007).

The aim of this note is to give a simplified proof of the surjectivity of the natural Milnor–Chow homomorphism ρ: KnM(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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