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The Hilbert Symbol in Higher-Dimensional Local Fields for Formal Lubin–Tate Groups. II

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In this paper, an explicit formula for the Hilbert pairing between the Milnor K-group of a higherdimensional local field and the higher-dimensional formal Lubin–Tate module is derived. This formula is a generalization of such a formula in the one-dimensional case. Here we consider the case of characteristic p > 0 of the penultimate residue field.

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References

  1. S. S. Afanas’eva, B. M. Bekker, and S. V. Vostokov, “The Hilbert symbol in higherdimensional local fields for a formal Lubin–Tate group,” Zap. Nauchn. Semin. POMI, 400, 20–49 (2012).

    Google Scholar 

  2. S. V. Vostokov, “An explicit form of the reciprocity law,” Izv. AN SSSR, Ser. Matem., 42, No. 6, 1288–1321 (1978).

    MathSciNet  MATH  Google Scholar 

  3. S. V. Vostokov, “Norm pairing in formal modules,” Izv. AN SSSR, Ser. Matem., 43, No. 4, 765–794 (1979).

    MathSciNet  Google Scholar 

  4. S. V. Vostokov and O. V. Demchenko, “An explicit formula for the Hilbert pairing for formal Honda groups,” Zap. Nauchn. Semin. POMI, 272, 86–128 (2000).

    Google Scholar 

  5. A. I. Madunts, “Formal Lubin–Tate groups over the ring of integers of a higher-dimensional local field,” Zap. Nauchn. Semin. POMI, 281, 221–226 (2001).

    Google Scholar 

  6. F. Lorenz and S. Vostokov, “Honda Groups and explicit pairings on the modules of Cartier curves,” Contemp. Math., 300, 143–170 (2002).

    Article  MathSciNet  Google Scholar 

  7. S. V. Vostokov and F. Lorenz, “An explicit formula for the Hilbert symbol for Honda groups in higher-dimensional local fields,” Mat. Sb., 194, No. 2, 3–36 (2003).

    Article  MathSciNet  Google Scholar 

  8. M. V. Bondarko, S. V. Vostokov, and F. Lorenz, “The Hilbert pairing for formal groups over σ-rings,” Zap. Nauchn. Semin. POMI, 319, 5–58 (2004).

    MATH  Google Scholar 

  9. D. G. Benua and S. V. Vostokov, “The arithmetic of the group of points of a formal group,” Zap. Nauchn. Semin. LOMI, 191, 9–23 (1991).

    MATH  Google Scholar 

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Authors and Affiliations

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

    S. S. Afanas’eva

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  1. S. S. Afanas’eva
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Correspondence to S. S. Afanas’eva.

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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 413, 2013, pp. 26–44.

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Afanas’eva, S.S. The Hilbert Symbol in Higher-Dimensional Local Fields for Formal Lubin–Tate Groups. II. J Math Sci 202, 346–359 (2014). https://doi.org/10.1007/s10958-014-2047-0

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