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Explicit constructions and the arithmetic of local number fields

  • S. V. VostokovEmail author
  • S. S. Afanas’eva
  • M. V. Bondarko
  • V. V. Volkov
  • O. V. Demchenko
  • E. V. Ikonnikova
  • I. B. Zhukov
  • I. I. Nekrasov
  • P. N. Pital’
Mathematics

Abstract

This is a survey of results obtained by members of the St. Petersburg school of local number theory headed by S.V. Vostokov during the past decades. All these results hardly fit into the title of the paper, since they involve a large circle of ideas, which are applied to an even larger class of problems of modern number theory. The authors tried to cover at least a small part of them, namely, those related to the modern approach to explicit expressions of the Hilbert symbol for nonclassical formal modules in the one- and higher-dimensional cases and their applications in local arithmetic geometry and ramification theory.

Keywords

formal groups reciprocity law local number fields higher local fields 

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Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  • S. V. Vostokov
    • 1
    Email author
  • S. S. Afanas’eva
    • 1
    • 2
  • M. V. Bondarko
    • 1
  • V. V. Volkov
    • 1
  • O. V. Demchenko
    • 1
  • E. V. Ikonnikova
    • 1
  • I. B. Zhukov
    • 1
  • I. I. Nekrasov
    • 1
  • P. N. Pital’
    • 1
  1. 1.St. Petersburg State UniversitySt. PetersburgRussia
  2. 2.Saint Petersburg National Research University of Information TechnologiesSt. PetersburgRussia

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