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St. Petersburg Mathematical Journal

This journal is a cover-to-cover translation into English of Algebra i Analiz, published six times a year by the mathematics section of the Russian Academy of Sciences.

ISSN 1547-7371 (online) ISSN 1061-0022 (print)

The 2020 MCQ for St. Petersburg Mathematical Journal is 0.68.

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Approximation approach to ramification theory
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by I. B. Zhukov and G. K. Pak
Translated by: I. B. Zhukov
St. Petersburg Math. J. 27 (2016), 967-976
DOI: https://doi.org/10.1090/spmj/1429
Published electronically: September 30, 2016
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Abstract:

A new approach is suggested to the theory of ramification in finite extensions of complete discrete valuation fields in the case of an imperfect residue field. It is based on the notion of a distance between extensions that shows the difference in ramification depths arising after a base change of a certain type. For two-dimensional local fields of prime characteristic, the following is proved. If the distance between two constant extensions (i.e., extensions defined over a given field with perfect residue field) is zero, then the corresponding Hasse–Herbrand functions coincide. The converse is verified only for extensions of degree $p$.
References
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Bibliographic Information
  • I. B. Zhukov
  • Affiliation: Department of Mathematics and Mechanics, St. Petersburg State University, Universitetskiĭ pr. 28, Petrodvorets, St. Petersburg 198504, Russia
  • Email: i.zhukov@spbu.ru
  • G. K. Pak
  • Affiliation: Institute of Mathematics and Computer Science, Far-East State University, Oktyabr′skaya ul. 27, 690000 Vladivostok, Russia
  • Email: pakgk@imcs.dvgu.ru
  • Received by editor(s): September 1, 2015
  • Published electronically: September 30, 2016
  • Additional Notes: Supported by RFBR (grant no. 14-01-00393-a)

    • Dedicated: to Sergey Vladimirovich Vostokov with deep gratitude
  • © Copyright 2016 American Mathematical Society
  • Journal: St. Petersburg Math. J. 27 (2016), 967-976
  • MSC (2010): Primary 11S15; Secondary 14E22
  • DOI: https://doi.org/10.1090/spmj/1429
  • MathSciNet review: 3589225