The Gersten conjecture for Milnor K-theory

By M. Kerz. 2008

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Milnor -theory of local rings with finite residue fields (2010, methodology): “The important fact about this motivic cohomology functor is that it is continuous, see Definition 5 where one has to assume that all appearing rings are regular.”
Aspects of Enumerative Geometry with Quadratic Forms (2017, background): “The purity isomorphism for EM(K M ∗ ) is a direct consequence of the Gersten resolution for KM ∗ [26].”
A DG Guide to Voevodsky’s Motives (2006, background): “M (X, Z). According to [ Ke ] (and [NS], lecture 5 of [MVW], where the case of a field is treated), this is an isomorphism.”
Slices of hermitian $K$–theory and Milnor's conjecture on quadratic forms (2013, methodology): “A further generalization to smooth semilocal rings containing a field of characteristic zero follows by the same method using Levine’s generalized Milnor conjecture on étale cohomology of semilocal rings [20], as shown in [11] and [18], cf.”