Milnor K-theory of complete discrete valuation rings with finite residue fields

摘要

AbstractConsider a complete discrete valuation ringOwith quotient fieldFand finite residue field. Then the inclusion mapO?Finduces a mapK??MO→K??MFon improved Milnor K-theory. We show that this map is an isomorphism in degrees bigger or equal to 3. This implies the Gersten conjecture for improved Milnor K-theory forO