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 $K$.