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An Explicit Form of the Hilbert Symbol for Polynomial Formal Groups Over a Multidimensional Local Field. I. / Vostokov, S. V.; Volkov, V.; Bondarko, M. V.

In: Journal of Mathematical Sciences (United States), Vol. 219, No. 3, 01.12.2016, p. 370-374.

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

Harvard

Vostokov, SV, Volkov, V & Bondarko, MV 2016, 'An Explicit Form of the Hilbert Symbol for Polynomial Formal Groups Over a Multidimensional Local Field. I', Journal of Mathematical Sciences (United States), vol. 219, no. 3, pp. 370-374. https://doi.org/10.1007/s10958-016-3112-7

APA

Vostokov, S. V., Volkov, V., & Bondarko, M. V. (2016). An Explicit Form of the Hilbert Symbol for Polynomial Formal Groups Over a Multidimensional Local Field. I. Journal of Mathematical Sciences (United States), 219(3), 370-374. https://doi.org/10.1007/s10958-016-3112-7

Vancouver

Vostokov SV, Volkov V, Bondarko MV. An Explicit Form of the Hilbert Symbol for Polynomial Formal Groups Over a Multidimensional Local Field. I. Journal of Mathematical Sciences (United States). 2016 Dec 1;219(3):370-374. https://doi.org/10.1007/s10958-016-3112-7

Author

Vostokov, S. V. ; Volkov, V. ; Bondarko, M. V. / An Explicit Form of the Hilbert Symbol for Polynomial Formal Groups Over a Multidimensional Local Field. I. In: Journal of Mathematical Sciences (United States). 2016 ; Vol. 219, No. 3. pp. 370-374.

BibTeX

@article{603d69cb35ef4988a67e3b521e61018b,
title = "An Explicit Form of the Hilbert Symbol for Polynomial Formal Groups Over a Multidimensional Local Field. I",
abstract = "Let K be a multidimensional local field with characteristic different from the characteristic of its residue field, c be a unit of K, and Fc(X, Y) = X +Y +cXY be a polynomial formal group, which defines the formal module Fc(M) over the maximal ideal of the ring of integers in K. Assume that K contains the group of roots of the isogeny [pm]c(X), which we denote by μFc,m. Let [InlineMediaObject not available: see fulltext.] be the multiplicative group of Cartier curves and [InlineMediaObject not available: see fulltext.]c be the formal analog of the module Fc(M). In the present paper, the formal symbol { ·, · }c : Kn([InlineMediaObject not available: see fulltext.])×[InlineMediaObject not available: see fulltext.]c → μFc,m is constructed and its basic properties are checked. This is the first step in the construction of an explicit formula for the Hilbert symbol.",
author = "Vostokov, {S. V.} and V. Volkov and Bondarko, {M. V.}",
note = "Vostokov, S.V., Volkov, V. & Bondarko, M.V. An Explicit Form of the Hilbert Symbol for Polynomial Formal Groups Over a Multidimensional Local Field. I. J Math Sci 219, 370–374 (2016). https://doi.org/10.1007/s10958-016-3112-7",
year = "2016",
month = dec,
day = "1",
doi = "10.1007/s10958-016-3112-7",
language = "English",
volume = "219",
pages = "370--374",
journal = "Journal of Mathematical Sciences",
issn = "1072-3374",
publisher = "Springer Nature",
number = "3",

}

RIS

TY - JOUR

T1 - An Explicit Form of the Hilbert Symbol for Polynomial Formal Groups Over a Multidimensional Local Field. I

AU - Vostokov, S. V.

AU - Volkov, V.

AU - Bondarko, M. V.

N1 - Vostokov, S.V., Volkov, V. & Bondarko, M.V. An Explicit Form of the Hilbert Symbol for Polynomial Formal Groups Over a Multidimensional Local Field. I. J Math Sci 219, 370–374 (2016). https://doi.org/10.1007/s10958-016-3112-7

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Let K be a multidimensional local field with characteristic different from the characteristic of its residue field, c be a unit of K, and Fc(X, Y) = X +Y +cXY be a polynomial formal group, which defines the formal module Fc(M) over the maximal ideal of the ring of integers in K. Assume that K contains the group of roots of the isogeny [pm]c(X), which we denote by μFc,m. Let [InlineMediaObject not available: see fulltext.] be the multiplicative group of Cartier curves and [InlineMediaObject not available: see fulltext.]c be the formal analog of the module Fc(M). In the present paper, the formal symbol { ·, · }c : Kn([InlineMediaObject not available: see fulltext.])×[InlineMediaObject not available: see fulltext.]c → μFc,m is constructed and its basic properties are checked. This is the first step in the construction of an explicit formula for the Hilbert symbol.

AB - Let K be a multidimensional local field with characteristic different from the characteristic of its residue field, c be a unit of K, and Fc(X, Y) = X +Y +cXY be a polynomial formal group, which defines the formal module Fc(M) over the maximal ideal of the ring of integers in K. Assume that K contains the group of roots of the isogeny [pm]c(X), which we denote by μFc,m. Let [InlineMediaObject not available: see fulltext.] be the multiplicative group of Cartier curves and [InlineMediaObject not available: see fulltext.]c be the formal analog of the module Fc(M). In the present paper, the formal symbol { ·, · }c : Kn([InlineMediaObject not available: see fulltext.])×[InlineMediaObject not available: see fulltext.]c → μFc,m is constructed and its basic properties are checked. This is the first step in the construction of an explicit formula for the Hilbert symbol.

UR - http://www.scopus.com/inward/record.url?scp=84992215281&partnerID=8YFLogxK

U2 - 10.1007/s10958-016-3112-7

DO - 10.1007/s10958-016-3112-7

M3 - Article

AN - SCOPUS:84992215281

VL - 219

SP - 370

EP - 374

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -

ID: 38481101