Abstract:
Based on the pairing on Cartier curves
explicitly constructed in the previous paper of the authors, an explicit formula for the Hilbert symbol is constructed in a multidimensional local field of
characteristic zero with residue field of positive
characteristic on the formal module of a one-dimensional
Honda formal group. In the proof a Shafarevich basis
on the formal module is constructed, and so-called integer
$\mu$-modules in two-dimensional local
rings of a special form ( $\mu$-rings) are studied.
Citation:
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
\Bibitem{VosLor03}
\by S.~V.~Vostokov, F.~Lorenz
\paper An explicit formula for the~Hilbert symbol for Honda
groups in a~multidimensional local field
\jour Sb. Math.
\yr 2003
\vol 194
\issue 2
\pages 165--197
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\crossref{https://doi.org/10.1070/SM2003v194n02ABEH000711}
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Linking options:
https://www.mathnet.ru/eng/sm711
https://doi.org/10.1070/SM2003v194n02ABEH000711
https://www.mathnet.ru/eng/sm/v194/i2/p3
This publication is cited in the following 5 articles:
S. V. Vostokov, R. P. Vostokova, S. V. Bezzateev, “Teoriya chisel i prilozheniya v kriptografii”, Chebyshevskii sb., 19:3 (2018), 61–73
S. V. Vostokov, V. V. Volkov, “Explicit form of the Hilbert symbol on polynomial formal module for multidimensional local field. II”, J. Math. Sci. (N. Y.), 222:4 (2017), 394–403
S. V. Vostokov, V. V. Volkov, M. V. Bondarko, “Explicit form of Hilbert symbol for polynomial formal groups over multidimensional local field. I”, J. Math. Sci. (N. Y.), 219:3 (2016), 370–374
S. S. Afanas'eva, “The Hilbert symbol in multidimensional local fields for Lubin–Tate formal groups. 2”, J. Math. Sci. (N. Y.), 202:3 (2014), 346–359
S. S. Afanas'eva, B. M. Bekker, S. V. Vostokov, “The Hilbert symbol in multi-dimensional local fields for Lubin–Tate formal groups”, J. Math. Sci. (N. Y.), 192:2 (2013), 137–153
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