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Zap. Nauchn. Sem. POMI, 2007, Volume 343, Pages 206–221 (Mi znsl116)  

This article is cited in 3 scientific papers (total in 3 papers)

Topological $K$-groups of two-dimensional local fields

O. Yu. Ivanova

Saint-Petersburg State University

Abstract: We consider a complete two-dimensional local field $K$ of mixed characteristic with finite second residue field and suppose that there exists a completely ramified extension $L$ of $K$ such that $L$ is a standard field. We prove that the rank of the quotient $U(1)K_2^{\mathrm{top}}K/T_K$, where $T_K$ is the closure of the torsion subgroup, is equal to the degree of the constant subfield of $K$ over $\mathbb Q_p$. I. B. Zhukov constructed a set of generators of this quotient in the case where $K$ is a standard field. In this paper, we consider two natural generalizations of this set and prove that one of them generates the whole group and the other generates its subgroup of finite index.

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English version:
Journal of Mathematical Sciences (New York), 2007, 147:5, 7088–7097

Bibliographic databases:

UDC: 512.5
Received: 30.10.2006

Citation: O. Yu. Ivanova, “Topological $K$-groups of two-dimensional local fields”, Problems in the theory of representations of algebras and groups. Part 15, Zap. Nauchn. Sem. POMI, 343, POMI, St. Petersburg, 2007, 206–221; J. Math. Sci. (N. Y.), 147:5 (2007), 7088–7097

Citation in format AMSBIB
\Bibitem{Iva07}
\by O.~Yu.~Ivanova
\paper Topological $K$-groups of two-dimensional local fields
\inbook Problems in the theory of representations of algebras and groups. Part~15
\serial Zap. Nauchn. Sem. POMI
\yr 2007
\vol 343
\pages 206--221
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl116}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2469418}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 147
\issue 5
\pages 7088--7097
\crossref{https://doi.org/10.1007/s10958-007-0531-5}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-36148959271}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. O. Yu. Ivanova, “The $\mathbb Z_p$-rank of a topological $K$-group”, St. Petersburg Math. J., 20:4 (2009), 569–591  mathnet  crossref  mathscinet  zmath  isi
    2. O. Yu. Ivanova, “Orders of topological generators of the $K$-group of a standard two-dimensional local field”, J. Math. Sci. (N. Y.), 156:6 (2009), 918–936  mathnet  crossref  zmath
    3. Vostokov S.V. Afanas'eva 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 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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