title: On a norm property of Hilbert symbol over polynomial formal module in multidimensional local field
metadata.name: dc.contributor.author
metadata.value: Volkov, Vladislav V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-01-05T17:33:41Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-01-05T17:33:41Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Volkov V. V. On a norm property of Hilbert symbol over polynomial formal module in multidimensional local field. Vestnik of Saint Petersburg University. Series 1. Mathematics. Mechanics. Astronomy, 2016, vol. 3 (61), issue 4, pp. 552–557.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2016.404
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/5895
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A polynomial formal group Fc(X, Y ) = X+Y +cXY over a two-dimensional local field K, which contains
  p-th root of unity, is considered. It acts naturally on the maximal ideal M of the ring of integers OK.
  There is a constructive Hilbert pairing {·, ·}c : K2(K)× Fc(M) →  ξ 
  c, where  ξ 
  c stands for a module of
  roots of [p]c (p-th degree isogeny of Fc) with respect to the formal summation. There is also a norm map
  of Milnor groups Norm: K2(L) → K2(K) for a two-dimensional local fields extension L/K. Elements
  of its image are called norms in K2(L). The main result of this work proves, in a constructive way, the
  so-called norm property of the pairing {·, ·}c: {x, β}c = 0 ⇐⇒ x is a norm in K2(K([p]
  −1
  c (β))), where
  [p]
  −1
  c (β) denotes roots of the equation [p]c = β. Refs 6.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при поддержке РНФ (грант 16-11-10200).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: Hilbert symbol
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: multidimensional local field
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: formal groups
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: polynomial formal group
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: norm property
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On a norm property of Hilbert symbol over polynomial formal module in multidimensional local field
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 04-Volkov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/5895/1/04-Volkov.pdf
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