TY - JOUR

T1 - An Explicit Form of the Hilbert Symbol for Polynomial Formal Groups Over a Multidimensional Local Field. I

AU - Vostokov, S. V.

AU - Volkov, V.

AU - Bondarko, M. V.

N1 - Vostokov, S.V., Volkov, V. & Bondarko, M.V. An Explicit Form of the Hilbert Symbol for Polynomial Formal Groups Over a Multidimensional Local Field. I. J Math Sci 219, 370–374 (2016). https://doi.org/10.1007/s10958-016-3112-7

PY - 2016/12/1

Y1 - 2016/12/1

N2 - Let K be a multidimensional local field with characteristic different from the characteristic of its residue field, c be a unit of K, and Fc(X, Y) = X +Y +cXY be a polynomial formal group, which defines the formal module Fc(M) over the maximal ideal of the ring of integers in K. Assume that K contains the group of roots of the isogeny [pm]c(X), which we denote by μFc,m. Let [InlineMediaObject not available: see fulltext.] be the multiplicative group of Cartier curves and [InlineMediaObject not available: see fulltext.]c be the formal analog of the module Fc(M). In the present paper, the formal symbol { ·, · }c : Kn([InlineMediaObject not available: see fulltext.])×[InlineMediaObject not available: see fulltext.]c → μFc,m is constructed and its basic properties are checked. This is the first step in the construction of an explicit formula for the Hilbert symbol.

AB - Let K be a multidimensional local field with characteristic different from the characteristic of its residue field, c be a unit of K, and Fc(X, Y) = X +Y +cXY be a polynomial formal group, which defines the formal module Fc(M) over the maximal ideal of the ring of integers in K. Assume that K contains the group of roots of the isogeny [pm]c(X), which we denote by μFc,m. Let [InlineMediaObject not available: see fulltext.] be the multiplicative group of Cartier curves and [InlineMediaObject not available: see fulltext.]c be the formal analog of the module Fc(M). In the present paper, the formal symbol { ·, · }c : Kn([InlineMediaObject not available: see fulltext.])×[InlineMediaObject not available: see fulltext.]c → μFc,m is constructed and its basic properties are checked. This is the first step in the construction of an explicit formula for the Hilbert symbol.

UR - http://www.scopus.com/inward/record.url?scp=84992215281&partnerID=8YFLogxK

U2 - 10.1007/s10958-016-3112-7

DO - 10.1007/s10958-016-3112-7

M3 - Article

AN - SCOPUS:84992215281

VL - 219

SP - 370

EP - 374

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 3

ER -