The Milnor-Chow homomorphism revisited
Moritz Kerz, Stefan Müller-Stach
Number | 17 |
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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.