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Zap. Nauchn. Sem. 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

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.

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English version:
Journal of Mathematical Sciences (New York), 2013, 192:2, 137–153

Bibliographic databases:

Document Type: Article
UDC: 512.741
Received: 28.11.2011

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://www.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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884986685}


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    This publication is cited in the following articles:
    1. S. S. Afanas'eva, “The Hilbert symbol in multidimensional local fields for Lubin–Tate formal groups. 2”, J. Math. Sci. (N. Y.), 202:3 (2014), 346–359  mathnet  crossref  mathscinet
    2. S. V. Vostokov, V. V. Volkov, M. V. Bondarko, “Explicit form of Hilbert symbol for polynomial formal groups over multidimensional local field. I”, J. Math. Sci. (N. Y.), 219:3 (2016), 370–374  mathnet  crossref  mathscinet
    3. S. V. Vostokov, V. V. Volkov, “Explicit form of the Hilbert symbol on polynomial formal module for multidimensional local field. II”, J. Math. Sci. (N. Y.), 222:4 (2017), 394–403  mathnet  crossref  mathscinet
    4. 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
  • Записки научных семинаров ПОМИ
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