Geodesic
Explicit form of Hilbert symbol for polynomial formal groups over multidimensional local field. I
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 27, Tome 430 (2014), pp. 53-60 
S. V. Vostokov; V. V. Volkov; M. V. Bondarko. Explicit form of Hilbert symbol for polynomial formal groups over multidimensional local field. I. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 27, Tome 430 (2014), pp. 53-60. http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a4/
@article{ZNSL_2014_430_a4,
     author = {S. V. Vostokov and V. V. Volkov and M. V. Bondarko},
     title = {Explicit form of {Hilbert} symbol for polynomial formal groups over multidimensional local {field.~I}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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     year = {2014},
     volume = {430},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_430_a4/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $K$ be a multidimensional local field with characteristic different from characteristic of its residue field, $c$ be a unit of $K$ and $F_c(X,Y)=X+Y+cXY$ be a polynomial formal group, which defines formal module $F_c(\mathfrak M)$ over maximal ideal of ring of integers in $K$. Assume that $K$ contains group of the roots of isogeny $[p^m]_c(X)$, which we denote by $\mu_{F_c,m}$. Let $\mathcal H$ be the multiplicative group of Cartier curves and $\mathcal H_c$ be a formal analogue of the module $F_c(\mathfrak M)$. In the current work we construct formal symbol $\{\cdot,\cdot\}_c\colon K_n(\mathcal H)\times\mathcal H_c\to\mu_{F_c,m}$ and check its basic properties. This is the first step in construction of the explicit formula for the Hilbert symbol.

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