Milnor $K$-groups modulo $p^{n}$ of a complete discrete valuation field

Abstract

For a mixed characteristic complete discrete valuation field $K$ which contains a $p^{n}$-th root of unity, we determine the graded quotients of the filtration on the Milnor $K$-groups $K_{q}^{M}(K)$ modulo $p^{n}$ in terms of differential forms of the residue field of $K$.