Geodesic
The Hilbert symbol in multi-dimensional local fields for Lubin–Tate formal groups
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 23, Tome 400 (2012), pp. 20-49 
S. S. Afanas'eva; B. M. Bekker; S. V. Vostokov. The Hilbert symbol in multi-dimensional local fields for Lubin–Tate formal groups. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 23, Tome 400 (2012), pp. 20-49. http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a1/
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     author = {S. S. Afanas'eva and B. M. Bekker and S. V. Vostokov},
     title = {The {Hilbert} symbol in multi-dimensional local fields for {Lubin{\textendash}Tate} formal groups},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     year = {2012},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a1/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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

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