Hilbert symbol in a discrete valuated field

descriptionPublicationkeyboard_double_arrow_right Article 01 May 1982 English Publisher:Springer Science and Business Media LLCJournal:Journal of Soviet Mathematics, volume 19, pages 1,006-1,019 (issn: 0090-4104, eissn: 1573-8795,

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Authors: Vostokov, S. V.;

doi: 10.1007/bf01476113

Hilbert symbol in a discrete valuated field

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Abstract

In a complete discrete valuated field of characteristic zero with perfect residue field of prime characteristic a pairing with values in the group of primary elements is defined. It is proved that this pairing agrees with the Hilbert norm residue symbol and therefore provides an explicit formula for the latter.

Keywords

Other nonanalytic theory, norm residue, Hilbert symbol, Units and factorization, Valued fields, complete discrete valued fields

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