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Zap. Nauchn. Sem. POMI, 2013, Volume 413, Pages 26–44 (Mi znsl5655)  

This article is cited in 1 scientific paper (total in 1 paper)

The Hilbert symbol in multidimensional local fields for Lubin–Tate formal groups. 2

S. S. Afanas'eva

St. Petersburg State University, St. Petersburg, Russia

Abstract: In this paper an explicit formula for the Hilbert pairing between the Milnor $K$-group of multidimensional local field and the multidimensional Lubin–Tate formal module is derived. This formula is a generalization of such formula in one-dimensional case. Here we consider the case of characteristic $p>0$ of penultimate residue field.

Key words and phrases: Lubi–Tate formal groups, Hilbert symbol, multidimensional local fields.

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English version:
Journal of Mathematical Sciences (New York), 2014, 202:3, 346–359

Bibliographic databases:

UDC: 512.741
Received: 28.11.2011

Citation: S. S. Afanas'eva, “The Hilbert symbol in multidimensional local fields for Lubin–Tate formal groups. 2”, Problems in the theory of representations of algebras and groups. Part 24, Zap. Nauchn. Sem. POMI, 413, POMI, St. Petersburg, 2013, 26–44; J. Math. Sci. (N. Y.), 202:3 (2014), 346–359

Citation in format AMSBIB
\Bibitem{Afa13}
\by S.~S.~Afanas'eva
\paper The Hilbert symbol in multidimensional local fields for Lubin--Tate formal groups.~2
\inbook Problems in the theory of representations of algebras and groups. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 413
\pages 26--44
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5655}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3073057}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 202
\issue 3
\pages 346--359
\crossref{https://doi.org/10.1007/s10958-014-2047-0}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919949997}


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    This publication is cited in the following articles:
    1. S. V. Vostokov, S. S. Afanas'eva, M. V. Bondarko, V. V. Volkov, O. V. Demchenko, E. V. Ikonnikova, I. B. Zhukov, I. I. Nekrasov, P. N. Pital, “Explicit constructions and the arithmetic of local number fields”, Vestnik St. Petersburg Univ. Math., 50:3 (2017), 242–264  crossref  mathscinet  isi  scopus
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