title: Explicit constructions and arithmetic of local number fields
metadata.name: dc.contributor.author
metadata.value: Vostokov, Sergei V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Afanaseva, Sofia S.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Bondarko, Mikhail V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Volkov, Vladislav V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Demchenko, Oleg V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Ikonnikova, Elena V.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Zhukov, Igor B.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Nekrasov, Ilia I.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Pital’, Petr N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-09-20T13:38:37Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-09-20T13:38:37Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Vostokov S.V., Afanaseva S. S., Bondarko M.V., Volkov V.V., Demchenko O.V., Ikonnikova E.V., Zhukov I.B., Nekrasov I. I., Pital’ P.N. Explicit constructions and arithmetic of local number fields. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2017, vol. 4 (62), issue 3, pp. 402– 435.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2017.305
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/7145
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: This paper is a survey of some of the results obtained by Saint Petersburg number theory school over recent
  decades. We consider explicit formulas for the Hilbert symbol in case of nonclassical formal modules and their applications in local arithmetic geometry and ramification theory. For topics studied by the school,
  but not included in this survey (due to the lack of space), references are given.
  In the section on explicit formulas, we present results for formal modules constructed using Honda
  formal group laws and polynomial formal group laws, and also the interpretation using p-adic integrals.
  Their implications concerning Galois modules are also described. We give the classification of formal group
  laws over local number fields as well. Further, we discuss constructions of complete discrete valuation fields’
  extensions. Besides some results in structure theory of higher local fields are presented. The last section
  is concerned with ramification theory for higher local fields. Refs 139.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой 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. Mathematics. Mechanics. Astronomy;Volume 4 (62); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: formal groups
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: reciprocity laws
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: local number fields
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: higher local fields
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Explicit constructions and arithmetic of local number fields
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 05-Vostokov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/7145/1/05-Vostokov.pdf
resources.format: Adobe PDF
resources.size: 495,19 kB