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Mat. Sb. (N.S.), 1950, Volume 26(68), Number 1, Pages 113–146 (Mi msb5872)  

This article is cited in 27 scientific papers (total in 27 papers)

A general reciprocity law

I. R. Shafarevich


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Received: 24.01.1949

Citation: I. R. Shafarevich, “A general reciprocity law”, Mat. Sb. (N.S.), 26(68):1 (1950), 113–146

Citation in format AMSBIB
\Bibitem{Sha50}
\by I.~R.~Shafarevich
\paper A general reciprocity law
\jour Mat. Sb. (N.S.)
\yr 1950
\vol 26(68)
\issue 1
\pages 113--146
\mathnet{http://mi.mathnet.ru/msb5872}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=31944}
\zmath{https://zbmath.org/?q=an:0036.15901}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. I. G. Zel'venskii, “On the algebraic closure of a local field for $p=2$”, Math. USSR-Izv., 6:5 (1972), 925–937  mathnet  crossref  mathscinet  zmath
    2. S. V. Vostokov, “An orthogonal basis of a local field”, Math. USSR-Izv., 7:6 (1973), 1225–1237  mathnet  crossref  mathscinet  zmath
    3. S. V. Vostokov, “Explicit form of the law of reciprocity”, Math. USSR-Izv., 13:3 (1979), 557–588  mathnet  crossref  mathscinet  zmath  isi
    4. S. V. Vostokov, “A norm pairing in formal modules”, Math. USSR-Izv., 15:1 (1980), 25–51  mathnet  crossref  mathscinet  zmath  isi
    5. V. A. Kolyvagin, “Formal groups and the norm residue symbol”, Math. USSR-Izv., 15:2 (1980), 289–348  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. 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
    7. V. A. Abrashkin, “Galois moduli of period $p$ group schemes over a ring of Witt vectors”, Math. USSR-Izv., 31:1 (1988), 1–46  mathnet  crossref  mathscinet  zmath
    8. L. V. Kuz'min, “Some remarks on the $l$-adic regulator. II”, Math. USSR-Izv., 35:1 (1990), 113–144  mathnet  crossref  mathscinet  zmath
    9. I. B. Fesenko, “Local class field theory: perfect residue field case”, Russian Acad. Sci. Izv. Math., 43:1 (1994), 65–81  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    10. V. A. Abrashkin, “Explicit formulae for the Hilbert symbol of a formal group over the Witt vectors”, Izv. Math., 61:3 (1997), 463–515  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. I. S. Rakhimov, “Arithmetic Invariants for a Class of Elliptic Curves”, Siberian Adv. Math., 14:2 (2004), 79–91  mathnet  mathscinet  zmath  elib
    12. Proc. Steklov Inst. Math., 241 (2003), 98–109  mathnet  mathscinet  zmath
    13. I. S. Rakhimov, “O povedenii arifmeticheskikh invariantov nekotorogo klassa ellipticheskikh krivykh v krugovykh $\Gamma$-rasshireniyakh”, Matem. tr., 8:1 (2005), 122–134  mathnet  mathscinet  zmath  elib
    14. S. V. Vostokov, “The classical reciprocity law for power residues as an analog of the Abelian integral theorem”, St. Petersburg Math. J., 20:6 (2009), 929–936  mathnet  crossref  mathscinet  zmath  isi  elib
    15. S. V. Vostokov, “Canonical basis of Hensel–Shafarevich in complete discrete valuation fields”, J. Math. Sci. (N. Y.), 188:5 (2013), 570–581  mathnet  crossref  mathscinet
    16. M. A. Ivanov, “Product of $p^n$-power residues as an Abelian integral”, St. Petersburg Math. J., 24:2 (2013), 275–281  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    17. S. V. Vostokov, M. A. Ivanov, “Integralnaya teorema Koshi i klassicheskii zakon vzaimnosti”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 154, no. 2, Izd-vo Kazanskogo un-ta, Kazan, 2012, 73–82  mathnet
    18. 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
    19. 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
    20. 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
    21. St. Petersburg Math. J., 26:6 (2015), 859–865  mathnet  crossref  mathscinet  isi  elib  elib
    22. 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
    23. 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
    24. 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
    25. A. I. Madunts, “Formal modules for relative Lubin–Tate formal groups”, J. Math. Sci. (N. Y.), 232:5 (2018), 704–716  mathnet  crossref  mathscinet
    26. Vostokov S., “Skew-symmetric pairing on polynomial formal modules”, Lobachevskii J. Math., 38:1 (2017), 170–176  crossref  isi
    27. Vostokov S.V., Afanas'eva S.S., Bondarko M.V., Volkov V.V., Demchenko O.V., Ikonnikova E.V., Zhukov I.B., Nekrasov I.I., Pital P.N., “Explicit Constructions and the Arithmetic of Local Number Fields”, Vestnik St. Petersburg Univ. Math., 50:3 (2017), 242–264  crossref  isi
  • Математический сборник (новая серия) - 1947–1963
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