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Journal of Mathematical Sciences

, Volume 232, Issue 5, pp 704–716 | Cite as

Formal Modules for Relative Formal Lubin–Tate Groups

  • A. I. Madunts
Article

Relative formal Lubin–Tate groups are studied, namely, their structure, the ring of endomorphisms, and the group of points. The primary elements are considered, and an explicit formula for the generalized Hilbert symbol is derived.

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References

  1. 1.
    M. Hazewinkel, Formal Groups and Applications, Acad. Press, New York (1978).Google Scholar
  2. 2.
    J. Lubin and J. Tate, “Formal complex multiplication in local fields,” Ann. Math. (2), 81, No. 2, 380–387 (1985).Google Scholar
  3. 3.
    E. de Shalite, “Relative Lubin–Tate groups,” Proc. Amer. Math. Soc., 95, No. 1, 1–4 (1985).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    S. V. Vostokov, “The norm pairing in formal modules,” Izv. AN SSSR, Ser. Mat., 45, No. 5, 985–1014 (1981).zbMATHGoogle Scholar
  5. 5.
    S. V. Vostokov, “The Hilbert symbol for formal Lubin–Tate groups. I,” Zap. Nauchn. Semin. LOMI, 114, 77–95 (1982).zbMATHGoogle Scholar
  6. 6.
    S. V. Vostokov and O. V. Demchenko, “An explicit form of the Hilbert pairing for relative formal Lubin–Tate groups,” Zap. Nauchn. Semin. POMI, 227, 41–44 (1995).zbMATHGoogle Scholar
  7. 7.
    S. V. Vostokov and I. B. Fesenko, “The Hilbert symbol for formal Lubin–Tate groups. II,” Zap. Nauchn. Semin. LOMI, 132, 85–96 (1983).zbMATHGoogle Scholar
  8. 8.
    S. V. Vostokov, “Symbols on formal groups,” Izv. AN SSSR, Ser. Mat., 45, No. 5, 9–23 (1981).MathSciNetzbMATHGoogle Scholar
  9. 9.
    S. V. Vostokov, “An explicit form of the reciprocity law,” Izv. AN SSSR, Ser. Mat., 42, No. 6, 1288–1321 (1978).MathSciNetzbMATHGoogle Scholar
  10. 10.
    K. Iwasawa, Local Class Field Theory [Russian translation], Mir, Moscow (1983).Google Scholar
  11. 11.
    A. I. Madunts, “On convergence of series over local fields,” Trudy SPb Mat. Obshch., 3, 283–320 (1994).MathSciNetGoogle Scholar
  12. 12.
    A. I. Madunts, “Convergence of sequences and series in multidimensional complete fields,” Author’s summary of the PhD Thesis, St. Petersburg (1995).Google Scholar
  13. 13.
    A. I. Madunts, “Formal Lubin–Tate groups over the ring of integers of a multidimensional local field,” Zap. Nauchn. Semin. POMI, 281, 221–226 (2001).MathSciNetzbMATHGoogle Scholar
  14. 14.
    A. I. Madunts and R. P. Vostokova, “Formal modules for generalized Lubin–Tate groups,” Zap. Nauchn. Semin. POMI, 435, 95–112 (2015).zbMATHGoogle Scholar
  15. 15.
    I. R. Shafarevich, “The general reciprocity law,” Mat. Sb., 26 (68), No. 1, 113–146 (1950).Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.St.Petersburg State UniversitySt. PetersburgRussia

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