title: Comparison of classifications of 2-dimensional local fields, type II
metadata.name: dc.contributor.author
metadata.value: Ivanova, Olga Yu.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Zhukov, Igor B.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2020-12-18T16:41:43Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2020-12-18T16:41:43Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2020-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Ivanova O. Yu., Zhukov I. B. Comparison of classifications of 2-dimensional local fields, type II. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2020, vol. 7 (65), issue 4, pp. 607–621.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/spbu01.2020.404
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/21845
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The article contributes to the theory of elimination of wild ramification for 2-dimensional
  local fields. It continues the study of classification of complete discrete valuation fields
  introduced in the work of Masato Kurihara. The main object of study is a 2-dimensional
  local field K of mixed characteristic with a finite residue field of odd characteristic. If such
  a field is weakly unramified over its constant subfield k (the maximal usual local field inside
  it), i. e., if eK/k = 1, its structure is well known. It is also known that any 2-dimensional
  local field can be turned into a standard one by means of a finite extension of its constant
  subfield (Epp’s theorem). However, the estimate of the minimal degree of such extension is
  an open question in general. In Kurihara’s article the 2-dimensional are subdivided into 2
  types as follows. Consider a non-trivial linear relation between differentials of the two local
  parameters of the field. The field belongs to Type I, if the valuation of the coefficient by
  the uniformizer is less than that by the second local parameter, and to Type II otherwise.
  This paper is devoted to the fields of Type II. For them we consider the invariant Δ, the
  difference between valuations of coefficients in the above mentioned linear relation (it is
  non-positive for the fields of Type II). The minimal degree of the required extension of k
  cannot be less than eK/k for trivial reasons. However, such extension of degree eK/k does
  not exist in general. In this article it is proved that it exists if the absolute value of Δ is
  sufficiently large. The corresponding estimate for Δ depends only on eK/k.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: This work was supported by Russian Science Foundation (grant no. 16-11-10200).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 7 (65); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: higher local fields
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: wild ramification
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Comparison of classifications of 2-dimensional local fields, type II
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 607-621.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/21845/1/607-621.pdf
resources.format: Adobe PDF
resources.size: 342,22 kB