A restriction isomorphism for zero-cycles with coefficients in Milnor K-theory

Abstract

We prove a restriction isomorphism for zero-cycles with coefficients in Milnor K-theory for smooth projective schemes over excellent henselian discrete valuation rings. Furthermore we relate zero-cycles with coefficients in Milnor K-theory to \'etale cohomology and certain Kato complexes and deduce finiteness results for zero-cycles with coefficients in Milnor K-theory over local fields.