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Izv. Akad. Nauk SSSR Ser. Mat., 1985, Volume 49, Issue 2, Pages 283–308 (Mi izv1355)  

This article is cited in 13 scientific papers (total in 13 papers)

Explicit construction of class field theory for a multidimensional local field

S. V. Vostokov


Abstract: Let $k$ be a finite extension of the field of $p$-adic numbers $\mathbf Q_p$ and $k\{\{t\}\}$ the field of Laurent series $\sum_{-\infty}^\infty a_it^i$ for which the $a_i$ are bounded in the norm of $k$ and $a_i\to0$ as $i\to-\infty$. In the $n$-dimensional local field $F=k\{\{t_1\}\}\cdots\{\{t_{n-1}\}\}$ a pairing is given in explicit form between the completed Milnor $k$-functor $K_n^{\mathrm{top}}(F)$ and the multiplicative group $F^*$ with values in the group of $q=p^m$th roots of unity.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1986, 26:2, 263–287

Bibliographic databases:

UDC: 519.48
MSC: Primary 11S31, 11S70; Secondary 11S10, 11S15
Received: 01.12.1983

Citation: S. V. Vostokov, “Explicit construction of class field theory for a multidimensional local field”, Izv. Akad. Nauk SSSR Ser. Mat., 49:2 (1985), 283–308; Math. USSR-Izv., 26:2 (1986), 263–287

Citation in format AMSBIB
\Bibitem{Vos85}
\by S.~V.~Vostokov
\paper Explicit construction of class field theory for a~multidimensional local field
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1985
\vol 49
\issue 2
\pages 283--308
\mathnet{http://mi.mathnet.ru/izv1355}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=791304}
\zmath{https://zbmath.org/?q=an:0608.12017}
\transl
\jour Math. USSR-Izv.
\yr 1986
\vol 26
\issue 2
\pages 263--287
\crossref{https://doi.org/10.1070/IM1986v026n02ABEH001141}


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  • http://mi.mathnet.ru/eng/izv/v49/i2/p283

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Fesenko I., “Abelian Local P-Class Field-Theory”, Math. Ann., 301:3 (1995), 561–586  crossref  mathscinet  zmath  isi
    2. Robert A. Bell, “On properties of the n-dimensional norm residue symbol in higher local class field theory”, Journal of Pure and Applied Algebra, 108:1 (1996), 1  crossref
    3. Robert A. Bell, “On the properties of the Vostokov and Parshin pairing in higher local class field theory”, Journal of Pure and Applied Algebra, 108:1 (1996), 7  crossref
    4. T. Fukaya, “Explicit reciprocity laws for <i>p</i>-divisible groups over higher dimensional local fields”, crll, 2001:531 (2001), 61  crossref  mathscinet  zmath  elib
    5. S. V. Vostokov, G. K. Pak, “Norm series in multidimensional local fields”, J. Math. Sci. (N. Y.), 130:3 (2005), 4675–4688  mathnet  crossref  mathscinet  zmath
    6. S. V. Vostokov, F. Lorenz, “An explicit formula for the Hilbert symbol for Honda groups in a multidimensional local field”, Sb. Math., 194:2 (2003), 165–197  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. M. V. Bondarko, S. V. Vostokov, F. Lorenz, “The Hilbert pairing for formal groups over $\sigma$-rings”, J. Math. Sci. (N. Y.), 134:6 (2006), 2445–2476  mathnet  crossref  mathscinet  zmath  elib  elib
    8. S. S. Afanas'eva, B. M. Bekker, S. V. Vostokov, “The Hilbert symbol in multi-dimensional local fields for Lubin–Tate formal groups”, J. Math. Sci. (N. Y.), 192:2 (2013), 137–153  mathnet  crossref  mathscinet
    9. S. V. Vostokov, “Shafarevich's paper “A general reciprocity law””, Sb. Math., 204:6 (2013), 781–800  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. E. V. Ikonnikova, E. V. Shaverdova, “The Shafarevich basis in higher dimensional local fields”, J. Math. Sci. (N. Y.), 202:3 (2014), 410–421  mathnet  crossref  mathscinet
    11. O. Yu. Ivanova, “Independent generators of the $K$-group of a standard $2$-dimensional field”, St. Petersburg Math. J., 26:4 (2015), 567–592  mathnet  crossref  mathscinet  isi  elib  elib
    12. 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
    13. 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
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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