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Approximation approach to ramification theory. / Zhukov, I. B.; Pak, G. K.

In: St. Petersburg Mathematical Journal, Vol. 27, No. 6, 01.01.2016, p. 967-976.

Research output: Contribution to journal › Article › peer-review

Harvard

Zhukov, IB & Pak, GK 2016, 'Approximation approach to ramification theory', St. Petersburg Mathematical Journal, vol. 27, no. 6, pp. 967-976. https://doi.org/10.1090/spmj/1429

APA

Zhukov, I. B., & Pak, G. K. (2016). Approximation approach to ramification theory. St. Petersburg Mathematical Journal, 27(6), 967-976. https://doi.org/10.1090/spmj/1429

Vancouver

Zhukov IB, Pak GK. Approximation approach to ramification theory. St. Petersburg Mathematical Journal. 2016 Jan 1;27(6):967-976. https://doi.org/10.1090/spmj/1429

Author

Zhukov, I. B. ; Pak, G. K. / Approximation approach to ramification theory. In: St. Petersburg Mathematical Journal. 2016 ; Vol. 27, No. 6. pp. 967-976.

BibTeX

@article{830857150123455ea6c22016bd7e563c,
title = "Approximation approach to ramification theory",
abstract = "A new approach is suggested to the theory of ramification in finite extensions of complete discrete valuation fields in the case of an imperfect residue field. It is based on the notion of a distance between extensions that shows the difference in ramification depths arising after a base change of a certain type. For two-dimensional local fields of prime characteristic, the following is proved. If the distance between two constant extensions (i.e., extensions defined over a given field with perfect residue field) is zero, then the corresponding Hasse-Herbrand functions coincide. The converse is verified only for extensions of degree p.",
keywords = "Higher local fields, Imperfect residue field, Ramification",
author = "Zhukov, {I. B.} and Pak, {G. K.}",
year = "2016",
month = jan,
day = "1",
doi = "10.1090/spmj/1429",
language = "English",
volume = "27",
pages = "967--976",
journal = "St. Petersburg Mathematical Journal",
issn = "1061-0022",
publisher = "American Mathematical Society",
number = "6",

}

RIS

TY - JOUR

T1 - Approximation approach to ramification theory

AU - Zhukov, I. B.

AU - Pak, G. K.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - A new approach is suggested to the theory of ramification in finite extensions of complete discrete valuation fields in the case of an imperfect residue field. It is based on the notion of a distance between extensions that shows the difference in ramification depths arising after a base change of a certain type. For two-dimensional local fields of prime characteristic, the following is proved. If the distance between two constant extensions (i.e., extensions defined over a given field with perfect residue field) is zero, then the corresponding Hasse-Herbrand functions coincide. The converse is verified only for extensions of degree p.

AB - A new approach is suggested to the theory of ramification in finite extensions of complete discrete valuation fields in the case of an imperfect residue field. It is based on the notion of a distance between extensions that shows the difference in ramification depths arising after a base change of a certain type. For two-dimensional local fields of prime characteristic, the following is proved. If the distance between two constant extensions (i.e., extensions defined over a given field with perfect residue field) is zero, then the corresponding Hasse-Herbrand functions coincide. The converse is verified only for extensions of degree p.

KW - Higher local fields

KW - Imperfect residue field

KW - Ramification

UR - http://www.scopus.com/inward/record.url?scp=84999288058&partnerID=8YFLogxK

U2 - 10.1090/spmj/1429

DO - 10.1090/spmj/1429

M3 - Article

AN - SCOPUS:84999288058

VL - 27

SP - 967

EP - 976

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 6

ER -

ID: 51971920