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

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Abstract

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.

Original languageEnglish
Pages (from-to)370-374
Number of pages5
JournalJournal of Mathematical Sciences (United States)
Volume219
Issue number3
Early online date24 Oct 2016
DOIs
StatePublished - 1 Dec 2016

Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics

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