Kurihara invariants and elimination of wild ramification

This article continues a series of works devoted to relation between two approaches to classification of complete discrete valuation fields with imperfect residue fields and in particular 2-dimensional local fields in the case of mixed characteristic. One of this approaches was introduced in the work of Masato Kurihara “On two types of complete discrete valuation fields” in terms of the module of differentials. Another one is based on Epp's theory of elimination of wild ramification.
We establish a lower bound for the degree of constant field extension that makes a given field into an almost standard one. This bound is expressed in terms of the invariant introduced in Kurihara's work.