Automorphisms of local fields of period $p^M$ and nilpotent class $
Victor Abrashkin · arXiv (Cornell University) · 2015
Suppose $K$ is a finite extension of $\mathbb{Q}_p$ containing a $p^M$-th primitive root of unity. For $1\leqslant se_K(M+s/(p-1))-(1-δ_{1s})/p$, where $e_K$ is the ramification index of $K$ and $δ_{1s}$ is the Kronecker symbol.