Abstract
The Steinberg relation for the classical Hilbert symbol is generalized to the Lubin–Tate formal groups. Necessary and sufficient conditions for the series satisfying the generalized Steinberg relation are obtained (in the paper such series are called norm series). Bibliography: 5 titles.
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REFERENCES
S. V. Vostokov, “A norm pairing in formal modules,” Izv. Akad. Nauk SSSR, Ser. Mat., 43, 765–794 (1979).
S. V. Vostokov, “Symbols on formal groups,” Izv. Akad. Nauk SSSR, Ser. Mat., 45, 985–1014 (1981).
S. V. Vostokov and I. B. Fesenko, “A certain property of the Hilbert pairing,” Mat. Zametki, 43,No. 3, 393–400 (1988).
V. A. Kolyvagin, “Formal groups and the norm residue symbol,” Izv. Akad. Nauk SSSR, Ser. Mat., 43, 1054–1120 (1979).
S. V. Vostokov, “An explicit form of the reciprocity law,” Izv. Akad. Nauk SSSR, Ser. Mat., 42, 1288–1321 (1978).
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Vostokov, S.V., Perlis, R. Norm Series for Lubin–Tate Formal Groups. Journal of Mathematical Sciences 120, 1549–1560 (2004). https://doi.org/10.1023/B:JOTH.0000017883.76167.65
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DOI: https://doi.org/10.1023/B:JOTH.0000017883.76167.65