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This article is cited in 13 scientific papers (total in 13 papers)
Formal groups and the norm residue symbol
V. A. Kolyvagin
Abstract:
This paper investigates the canonical pairing associated with a one-dimensional formal group law $F$ over the ring of integers of a finite extension of $\mathbf Q_p$ and an isogeny $f\colon F\to F$, just as the Hilbert symbol is associated with the multiplicative law and the isogeny “raising to the $p$th power”. Formulas are obtained which generalize the formulas of Artin–Hasse, Iwasawa, and Wiles. The formulas describe the values of the symbol in terms of $p$-adic differentiation, the logarithm of the formal group law, the norm, and the trace.
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Mathematics of the USSR-Izvestiya, 1980, 15:2, 289–348
Bibliographic databases:
   
UDC:
519.4
MSC: Primary 12B10; Secondary 12B15
Received: 25.12.1978
Citation:
V. A. Kolyvagin, “Formal groups and the norm residue symbol”, Izv. Akad. Nauk SSSR Ser. Mat., 43:5 (1979), 1054–1120; Math. USSR-Izv., 15:2 (1980), 289–348
Citation in format AMSBIB
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\jour Math. USSR-Izv.
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\pages 289--348
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Linking options:
http://mi.mathnet.ru/eng/izv1748 http://mi.mathnet.ru/eng/izv/v43/i5/p1054
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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S. V. Vostokov, “Symbols on formal groups”, Math. USSR-Izv., 19:2 (1982), 261–284
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V. A. Abrashkin, “Explicit formulae for the Hilbert symbol of a formal group over the Witt vectors”, Izv. Math., 61:3 (1997), 463–515
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T. Fukaya, “Explicit reciprocity laws for $p$-divisible groups over higher dimensional local fields”, crll, 2001:531 (2001), 61
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V. A. Kolyvagin, “Fermat's equation over the tower of cyclotomic fields”, Izv. Math., 65:3 (2001), 503–541
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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
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S. V. Vostokov, G. K. Pak, “Norm series in multidimensional local fields”, J. Math. Sci. (N. Y.), 130:3 (2005), 4675–4688
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S. V. Vostokov, E. V. Ferens-Sorotskiy, “Hilbert pairing for the polynomial formal groups”, Vestnik St Petersb Univ Math, 43:1 (2010), 18
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S. S. Afanas'eva, G. K. Pak, “Norm series for Honda formal groups”, J. Math. Sci. (N. Y.), 183:5 (2012), 577–583
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S. S. Afanas'eva, “Norm series for multi-dimensional Honda formal groups”, J. Math. Sci. (N. Y.), 192:2 (2013), 127–136
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St. Petersburg Math. J., 26:6 (2015), 859–865
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S. V. Vostokov, I. I. Nekrasov, “Lubin–Tate formal module in a cyclic unramified $p$-extension as Galois module”, J. Math. Sci. (N. Y.), 219:3 (2016), 375–379
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D. A. Malinin, “One construction of integral representations of $p$-groups and some applications”, Chebyshevskii sb., 16:3 (2015), 322–338
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S. V. Vostokov, I. L. Klimovitskii, P. N. Pital, “Universal Approach to the Arithmetics of Formal Groups”, Math. Notes, 104:2 (2018), 204–209
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