Kurihara classification and maximal depth extensions for multidimensional local fields
Olga Yu. Ivanova · St Petersburg Mathematical Journal · 2013
Multidimensional local fields of mixed characteristic with finite last residue field are considered. For each field and a set of its local parameters, a quantity $\Delta$ is defined as the difference of the minimum valuation of the coefficients at the differentials of local parameters of the residue field and the valuation of the coefficient at the differential of the uniformizer in a linear relation between the local parameters. In terms of the theory of elimination of ramification, the fields are described for which $\Delta$ attains its minimum for a fixed ramification index over the subfield of constants. The extreme values of $\Delta$ for a fixed field are studied.