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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 400, Pages 20–49 (Mi znsl5610)  
This article is cited in 4 scientific papers (total in 4 papers)

The Hilbert symbol in multi-dimensional local fields for Lubin–Tate formal groups

S. S. Afanas'eva, B. M. Bekker, S. V. Vostokov

Saint-Petersburg State University, Saint-Petersburg, Russia
Full-text PDF (386 kB) Citations (4)
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Abstract: In this paper an explicit formula for the Hilbert pairing between the Milnor $K$-group of a multi-dimensional local field and the multi-dimensional Lubin–Tate formal module is derived. This formula is a generalization of such a formula in one-dimensional case. Here we consider the case, where the penultimate residue field is of characteristic zero.
Key words and phrases: Lubin–Tate formal groups, Hilbert symbol, multi-dimensional local fields.
Received: 28.11.2011
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 192, Issue 2, Pages 137–153
DOI: https://doi.org/10.1007/s10958-013-1380-z
Bibliographic databases:
Document Type: Article
UDC: 512.741
Language: Russian
Citation: S. S. Afanas'eva, B. M. Bekker, S. V. Vostokov, “The Hilbert symbol in multi-dimensional local fields for Lubin–Tate formal groups”, Problems in the theory of representations of algebras and groups. Part 23, Zap. Nauchn. Sem. POMI, 400, POMI, St. Petersburg, 2012, 20–49; J. Math. Sci. (N. Y.), 192:2 (2013), 137–153
Citation in format AMSBIB
\Bibitem{AfaBekVos12}
\by S.~S.~Afanas'eva, B.~M.~Bekker, S.~V.~Vostokov
\paper The Hilbert symbol in multi-dimensional local fields for Lubin--Tate formal groups
\inbook Problems in the theory of representations of algebras and groups. Part~23
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 400
\pages 20--49
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5610}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3029564}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 192
\issue 2
\pages 137--153
\crossref{https://doi.org/10.1007/s10958-013-1380-z}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884986685}
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    This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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