The Milnor-Chow homomorphism revisited, by Moritz Kerz and Stefan Mueller-Stach

The aim of this note is to give a simplified proof of the surjectivity of the natural Milnor-Chow homomorphism between Milnor K-theory and higher Chow groups for essentially smooth (semi-)local k-algebras A with k infinite. 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.


Moritz Kerz <m.kerz@dpmms.cam.ac.uk>
Stefan Mueller-Stach <mueller-stach@uni-mainz.de>