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
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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.
@article{ZNSL_2012_400_a1,
author = {S. S. Afanas'eva and B. M. Bekker and S. V. Vostokov},
title = {The {Hilbert} symbol in multi-dimensional local fields for {Lubin--Tate} formal groups},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {20--49},
publisher = {mathdoc},
volume = {400},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a1/}
}
TY - JOUR AU - S. S. Afanas'eva AU - B. M. Bekker AU - S. V. Vostokov TI - The Hilbert symbol in multi-dimensional local fields for Lubin--Tate formal groups JO - Zapiski Nauchnykh Seminarov POMI PY - 2012 SP - 20 EP - 49 VL - 400 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a1/ LA - ru ID - ZNSL_2012_400_a1 ER -
%0 Journal Article %A S. S. Afanas'eva %A B. M. Bekker %A S. V. Vostokov %T The Hilbert symbol in multi-dimensional local fields for Lubin--Tate formal groups %J Zapiski Nauchnykh Seminarov POMI %D 2012 %P 20-49 %V 400 %I mathdoc %U http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a1/ %G ru %F ZNSL_2012_400_a1
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/