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Norm Series in High-Dimensional Local Fields

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In the present paper, the notion of norm series with respect to the norm residue symbol is generalized to high-dimensional local fields. Necessary and sufficient conditions for the existence of norm series are obtained. Bibliography: 12 titles.

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REFERENCES

  1. S. V. Vostokov and R. Perlis, “Norm series for Lubin-Tate formal groups,” Zap. Nauchn. Semin. POMI, 281, 105–127 (2001).

    Google Scholar 

  2. S. V. Vostokov, “An explicit construction of class field theory for high-dimensional local fields,” Izv. AN SSSR, Ser. Mat., 49, No.2, 283–308 (1985).

    Google Scholar 

  3. S. V. Vostokov, I. B. Zhukov, and I. B. Fesenko, “On the theory of high-dimensional local fields. Methods and constructions,” Algebra Analiz, 2, No.4, 91–118 (1990).

    Google Scholar 

  4. F. Lorenz and S. Vostokov, “Honda groups and explicit pairings on the modules of Cartier curves,” Contemporary Mathematics, 300, 143–170 (2002).

    Google Scholar 

  5. K. Kato, “A generalization of local class field theory by using K-groups. I,” J. Fac. Sci. Univ. Tokyo, Sec. IA, 26, 303–376 (1979); II, J. Fac. Sci. Univ. Tokyo, Sec. IA, 27, 603–683 (1980).

    Google Scholar 

  6. A. N. Parshin, “Class field theory and algebraic K-theory,” Usp. Mat. Nauk, 30, 253–254 (1975).

    Google Scholar 

  7. A. N. Parshin, “Local class field theory,” Trudy Mat. Inst. AN SSSR, 165, 143–170 (1984).

    Google Scholar 

  8. T. B. Belyaeva and S. V. Vostokov, “The Hilbert symbol in a complete high-dimensional field. II,” Zap. Nauchn. Semin. POMI, 281, 5–34 (2001).

    Google Scholar 

  9. A. I. Madunts, “Convergence of series over local fields,” Zap. Nauchn. Semin. LOMI, 198, 28–30 (1991).

    Google Scholar 

  10. S. V. Vostokov, “An explicit form of the reciprocity law,” Izv. AN SSSR, Ser. Mat., 42, No.6, 1287–1320 (1978).

    Google Scholar 

  11. G. Henniart, “Sur les lois de reciprocite explicites. I,” J. Reine Angew. Math., 329, 172–203 (1981).

    Google Scholar 

  12. V. A. Kolyvagin, “Formal groups and the norm residue symbol,” Izv. AN SSSR, Ser. Mat., 43, 1064–1120 (1979).

    Google Scholar 

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    S. V. Vostokov & G. K. Pak

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  1. S. V. Vostokov
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  2. G. K. Pak
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 305, 2003, pp. 60–83.

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Vostokov, S.V., Pak, G.K. Norm Series in High-Dimensional Local Fields. J Math Sci 130, 4675–4688 (2005). https://doi.org/10.1007/s10958-005-0362-1

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