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For a mixed characteristic complete discrete valuation field $K$ whichcontains a $p^n$-th root of unity, we determine the graded quotients of thefiltration on the Milnor $K$-groups $K_q^M(K)$ modulo $p^n$ in terms ofdifferential forms of the residue field of $K$.

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