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On ramification theory in the imperfect residue field case. / Zhukov, I. B.

In: Sbornik Mathematics, Vol. 194, No. 11-12, 01.01.2003, p. 1747-1774.

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

Harvard

Zhukov, IB 2003, 'On ramification theory in the imperfect residue field case', Sbornik Mathematics, vol. 194, no. 11-12, pp. 1747-1774.

APA

Zhukov, I. B. (2003). On ramification theory in the imperfect residue field case. Sbornik Mathematics, 194(11-12), 1747-1774.

Vancouver

Zhukov IB. On ramification theory in the imperfect residue field case. Sbornik Mathematics. 2003 Jan 1;194(11-12):1747-1774.

Author

Zhukov, I. B. / On ramification theory in the imperfect residue field case. In: Sbornik Mathematics. 2003 ; Vol. 194, No. 11-12. pp. 1747-1774.

BibTeX

@article{c31631c221b04cc89b4cc5812dcf3b66,
title = "On ramification theory in the imperfect residue field case",
abstract = "This paper is devoted to the ramification theory of complete discrete valuation fields such that the residue field has prime characteristic p and the cardinality of a p-base is 1. This class contains two-dimensional local and local-global fields. A new definition of ramification filtration for such fields is given. It turns out that Hasse-Herbrand type functions can be defined with all the usual properties. Thanks to this, a theory of upper ramification groups and the ramification theory of infinite extensions can be developed. The case of two-dimensional local fields of equal characteristic is studied in detail. A filtration on the second K-group of the field in question is introduced that is different from the one induced by the standard filtration on the multiplicative group. The reciprocity map of two-dimensional local class field theory is proved to identify this filtration with the ramification filtration.",
author = "Zhukov, {I. B.}",
year = "2003",
month = jan,
day = "1",
language = "English",
volume = "194",
pages = "1747--1774",
journal = "Sbornik Mathematics",
issn = "1064-5616",
publisher = "Turpion Ltd.",
number = "11-12",

}

RIS

TY - JOUR

T1 - On ramification theory in the imperfect residue field case

AU - Zhukov, I. B.

PY - 2003/1/1

Y1 - 2003/1/1

N2 - This paper is devoted to the ramification theory of complete discrete valuation fields such that the residue field has prime characteristic p and the cardinality of a p-base is 1. This class contains two-dimensional local and local-global fields. A new definition of ramification filtration for such fields is given. It turns out that Hasse-Herbrand type functions can be defined with all the usual properties. Thanks to this, a theory of upper ramification groups and the ramification theory of infinite extensions can be developed. The case of two-dimensional local fields of equal characteristic is studied in detail. A filtration on the second K-group of the field in question is introduced that is different from the one induced by the standard filtration on the multiplicative group. The reciprocity map of two-dimensional local class field theory is proved to identify this filtration with the ramification filtration.

AB - This paper is devoted to the ramification theory of complete discrete valuation fields such that the residue field has prime characteristic p and the cardinality of a p-base is 1. This class contains two-dimensional local and local-global fields. A new definition of ramification filtration for such fields is given. It turns out that Hasse-Herbrand type functions can be defined with all the usual properties. Thanks to this, a theory of upper ramification groups and the ramification theory of infinite extensions can be developed. The case of two-dimensional local fields of equal characteristic is studied in detail. A filtration on the second K-group of the field in question is introduced that is different from the one induced by the standard filtration on the multiplicative group. The reciprocity map of two-dimensional local class field theory is proved to identify this filtration with the ramification filtration.

UR - http://www.scopus.com/inward/record.url?scp=1642283245&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:1642283245

VL - 194

SP - 1747

EP - 1774

JO - Sbornik Mathematics

JF - Sbornik Mathematics

SN - 1064-5616

IS - 11-12

ER -

ID: 51972179