In this paper, an explicit formula for the Hilbert pairing between the Milnor K-group of a higher-dimensional local field and the higher-dimensional Lubin−tate formal module is derived. This formula is a generalization of such a formula in the one-dimensional case. Here the case where the penultimate residue field is of characteristic zero is considered. Bibliography: 11 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 400, 2012, pp. 20−49.
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Afanas’eva, S.S., Bekker, B.M. & Vostokov, S.V. The Hilbert Symbol in Higher-Dimensional Local Fields for Formal Lubin−Tate Groups. J Math Sci 192, 137–153 (2013). https://doi.org/10.1007/s10958-013-1380-z
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DOI: https://doi.org/10.1007/s10958-013-1380-z