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Zap. Nauchn. Sem. POMI, 2013, Volume 413, Pages 115–133 (Mi znsl5660)  

This article is cited in 2 scientific papers (total in 2 papers)

The Shafarevich basis in higher dimensional local fields

E. V. Ikonnikova, E. V. Shaverdova

St. Petersburg State University, St. Petersburg, Russia

Abstract: This paper presents a generalization of Shafarevich basis for $n$-dimensional local fields with perfect last residue field. We consider the group of principal units of such fields and construct its multiplicative basis.

Key words and phrases: higher dimensional local fields, the Shafarevich basis.

Full text: PDF file (289 kB)
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English version:
Journal of Mathematical Sciences (New York), 2014, 202:3, 410–421

Bibliographic databases:

Document Type: Article
UDC: 512.625
Received: 20.12.2012

Citation: E. V. Ikonnikova, E. V. Shaverdova, “The Shafarevich basis in higher dimensional local fields”, Problems in the theory of representations of algebras and groups. Part 24, Zap. Nauchn. Sem. POMI, 413, POMI, St. Petersburg, 2013, 115–133; J. Math. Sci. (N. Y.), 202:3 (2014), 410–421

Citation in format AMSBIB
\Bibitem{IkoSha13}
\by E.~V.~Ikonnikova, E.~V.~Shaverdova
\paper The Shafarevich basis in higher dimensional local fields
\inbook Problems in the theory of representations of algebras and groups. Part~24
\serial Zap. Nauchn. Sem. POMI
\yr 2013
\vol 413
\pages 115--133
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5660}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3073061}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2014
\vol 202
\issue 3
\pages 410--421
\crossref{https://doi.org/10.1007/s10958-014-2051-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84919914831}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. V. Ikonnikova, “Hensel–Shafarevich canonical basis in Lubin–Tate formal modules”, J. Math. Sci. (N. Y.), 219:3 (2016), 462–472  mathnet  crossref  mathscinet
    2. S. V. Vostokov, 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, “Explicit constructions and the arithmetic of local number fields”, Vestnik St. Petersburg Univ. Math., 50:3 (2017), 242–264  crossref  mathscinet  isi  scopus
  • Записки научных семинаров ПОМИ
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