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Mat. Sb., 2003, Volume 194, Number 2, Pages 3–36 (Mi msb711)  

This article is cited in 4 scientific papers (total in 4 papers)

An explicit formula for the Hilbert symbol for Honda groups in a multidimensional local field

S. V. Vostokova, F. Lorenzb

a Saint-Petersburg State University
b Westfälische Wilhelms-Universität Münster

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.

DOI: https://doi.org/10.4213/sm711

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English version:
Sbornik: Mathematics, 2003, 194:2, 165–197

Bibliographic databases:

UDC: 512.741
MSC: Primary 11S31; Secondary 14L05
Received: 04.06.2002

Citation: S. V. Vostokov, F. Lorenz, “An explicit formula for the Hilbert symbol for Honda groups in a multidimensional local field”, Mat. Sb., 194:2 (2003), 3–36; Sb. Math., 194:2 (2003), 165–197

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. 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  mathnet  crossref  mathscinet
    2. 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  mathnet  crossref  mathscinet
    3. 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  mathnet  crossref  mathscinet
    4. 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  mathnet  crossref  mathscinet
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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