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Explicit constructions and the arithmetic of local number fields. / Vostokov, S. V.; Afanas’eva, S. S.; Bondarko, M. V.; Volkov, V. V.; Demchenko, O. V.; Ikonnikova, E. V.; Zhukov, I. B.; Nekrasov, I. I.; Pital’, P. N.

In: Vestnik St. Petersburg University: Mathematics, Vol. 50, No. 3, 01.07.2017, p. 242-264.

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

Harvard

Vostokov, SV, Afanas’eva, SS, Bondarko, MV, Volkov, VV, Demchenko, OV, Ikonnikova, EV, Zhukov, IB, Nekrasov, II & Pital’, PN 2017, 'Explicit constructions and the arithmetic of local number fields', Vestnik St. Petersburg University: Mathematics, vol. 50, no. 3, pp. 242-264. https://doi.org/10.3103/S1063454117030128

APA

Vostokov, S. V., Afanas’eva, S. S., Bondarko, M. V., Volkov, V. V., Demchenko, O. V., Ikonnikova, E. V., Zhukov, I. B., Nekrasov, I. I., & Pital’, P. N. (2017). Explicit constructions and the arithmetic of local number fields. Vestnik St. Petersburg University: Mathematics, 50(3), 242-264. https://doi.org/10.3103/S1063454117030128

Vancouver

Vostokov SV, Afanas’eva SS, Bondarko MV, Volkov VV, Demchenko OV, Ikonnikova EV et al. Explicit constructions and the arithmetic of local number fields. Vestnik St. Petersburg University: Mathematics. 2017 Jul 1;50(3):242-264. https://doi.org/10.3103/S1063454117030128

Author

Vostokov, S. V. ; Afanas’eva, S. S. ; Bondarko, M. V. ; Volkov, V. V. ; Demchenko, O. V. ; Ikonnikova, E. V. ; Zhukov, I. B. ; Nekrasov, I. I. ; Pital’, P. N. / Explicit constructions and the arithmetic of local number fields. In: Vestnik St. Petersburg University: Mathematics. 2017 ; Vol. 50, No. 3. pp. 242-264.

BibTeX

@article{dd946d1e2b9047f9a4d16ba03a138227,
title = "Explicit constructions and the arithmetic of local number fields",
abstract = "This is a survey of results obtained by members of the St. Petersburg school of local number theory headed by S.V. Vostokov during the past decades. All these results hardly fit into the title of the paper, since they involve a large circle of ideas, which are applied to an even larger class of problems of modern number theory. The authors tried to cover at least a small part of them, namely, those related to the modern approach to explicit expressions of the Hilbert symbol for nonclassical formal modules in the one- and higher-dimensional cases and their applications in local arithmetic geometry and ramification theory.",
keywords = "formal groups, higher local fields, local number fields, reciprocity law",
author = "Vostokov, {S. V.} and Afanas{\textquoteright}eva, {S. S.} and Bondarko, {M. V.} and Volkov, {V. V.} and Demchenko, {O. V.} and Ikonnikova, {E. V.} and Zhukov, {I. B.} and Nekrasov, {I. I.} and Pital{\textquoteright}, {P. N.}",
year = "2017",
month = jul,
day = "1",
doi = "10.3103/S1063454117030128",
language = "English",
volume = "50",
pages = "242--264",
journal = "Vestnik St. Petersburg University: Mathematics",
issn = "1063-4541",
publisher = "Pleiades Publishing",
number = "3",

}

RIS

TY - JOUR

T1 - Explicit constructions and the arithmetic of local number fields

AU - Vostokov, S. V.

AU - Afanas’eva, S. S.

AU - Bondarko, M. V.

AU - Volkov, V. V.

AU - Demchenko, O. V.

AU - Ikonnikova, E. V.

AU - Zhukov, I. B.

AU - Nekrasov, I. I.

AU - Pital’, P. N.

PY - 2017/7/1

Y1 - 2017/7/1

N2 - This is a survey of results obtained by members of the St. Petersburg school of local number theory headed by S.V. Vostokov during the past decades. All these results hardly fit into the title of the paper, since they involve a large circle of ideas, which are applied to an even larger class of problems of modern number theory. The authors tried to cover at least a small part of them, namely, those related to the modern approach to explicit expressions of the Hilbert symbol for nonclassical formal modules in the one- and higher-dimensional cases and their applications in local arithmetic geometry and ramification theory.

AB - This is a survey of results obtained by members of the St. Petersburg school of local number theory headed by S.V. Vostokov during the past decades. All these results hardly fit into the title of the paper, since they involve a large circle of ideas, which are applied to an even larger class of problems of modern number theory. The authors tried to cover at least a small part of them, namely, those related to the modern approach to explicit expressions of the Hilbert symbol for nonclassical formal modules in the one- and higher-dimensional cases and their applications in local arithmetic geometry and ramification theory.

KW - formal groups

KW - higher local fields

KW - local number fields

KW - reciprocity law

UR - http://www.scopus.com/inward/record.url?scp=85029154804&partnerID=8YFLogxK

U2 - 10.3103/S1063454117030128

DO - 10.3103/S1063454117030128

M3 - Article

AN - SCOPUS:85029154804

VL - 50

SP - 242

EP - 264

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 3

ER -

ID: 35957072