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Izv. Akad. Nauk SSSR Ser. Mat., 1981, Volume 45, Issue 5, Pages 985–1014 (Mi izv1595)  

This article is cited in 5 scientific papers (total in 5 papers)

Symbols on formal groups

S. V. Vostokov


Abstract: The theory of a continuous Steinberg symbol in a local field is generalized to formal commutative groups. For Lubin–Tate groups, a universal symbol is constructed in explicit form, and it is shown that the module of values of an arbitrary symbol imbeds into the group of points of the formal group.
By means of this theory of symbols a new approach is given to obtaining an explicit form for the Hilbert norm residue symbol on Lubin–Tate formal groups.
Bibliography: 10 titles.

Full text: PDF file (2752 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1982, 19:2, 261–284

Bibliographic databases:

UDC: 519.48
MSC: Primary 12B25; Secondary 14L05
Received: 20.02.1981

Citation: S. V. Vostokov, “Symbols on formal groups”, Izv. Akad. Nauk SSSR Ser. Mat., 45:5 (1981), 985–1014; Math. USSR-Izv., 19:2 (1982), 261–284

Citation in format AMSBIB
\Bibitem{Vos81}
\by S.~V.~Vostokov
\paper Symbols on formal groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1981
\vol 45
\issue 5
\pages 985--1014
\mathnet{http://mi.mathnet.ru/izv1595}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=637613}
\zmath{https://zbmath.org/?q=an:0501.14027|0483.14011}
\transl
\jour Math. USSR-Izv.
\yr 1982
\vol 19
\issue 2
\pages 261--284
\crossref{https://doi.org/10.1070/IM1982v019n02ABEH001417}


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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. S. V. Vostokov, “Explicit construction of class field theory for a multidimensional local field”, Math. USSR-Izv., 26:2 (1986), 263–287  mathnet  crossref  mathscinet  zmath
    2. S. V. Vostokov, V. V. Volkov, “Explicit formula for Hilbert pairing on polynomial formal modules”, St. Petersburg Math. J., 26:5 (2015), 785–796  mathnet  crossref  mathscinet  isi  elib  elib
    3. A. I. Madunts, R. P. Vostokova, “Formal modules for generalized Lubin–Tate groups”, J. Math. Sci. (N. Y.), 219:4 (2016), 553–564  mathnet  crossref  mathscinet
    4. A. I. Madunts, “Formal modules for relative Lubin–Tate formal groups”, J. Math. Sci. (N. Y.), 232:5 (2018), 704–716  mathnet  crossref  mathscinet
    5. Vostokov S., “Skew-symmetric pairing on polynomial formal modules”, Lobachevskii J. Math., 38:1 (2017), 170–176  crossref  isi  scopus
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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