On the relationship between Kurihara’s classification and the theory of ramification removal

Abstract:

A complete two-dimensional mixed-characteristic local field with finite second residue field is considered. It is proved that such a field is standard if and only if the difference between the valuations of the coefficients of a linear relation between local parameters is infinite for some choice of local parameters; the field in question is almost standard if and only if the above-mentioned difference can be made arbitrarily large by changing local parameters. In the case where a given field can be extended to a standard field by a fierce extension of prime degree, the field type in Kurihara’s classification is proved to depend only on the ratio of the ramification jumps of these fields over their maximal standard subfields.