RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Izv. RAN. Ser. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Izv. Akad. Nauk SSSR Ser. Mat., 1975, Volume 39, Issue 3, Pages 487–495 (Mi izv2038)  

This article is cited in 6 scientific papers (total in 6 papers)

Cohomological dimension of some Galois groups

L. V. Kuz'min


Abstract: Suppose that $l$ is a prime number, $k$ is an algebraic number field containing a primitive root $\zeta_l$ ($\zeta_4$ if $l=2$), $S$ is a finite set of places of $k$ which contains all divisors of $l$, $K$ is the maximal $l$-extension of $k$ unramified outside $S$, $k_\infty$ is an arbitrary $\Gamma$-extension of $k$, and $H=G(K/k_\infty$. In this paper we find necessary and sufficient conditions for the group $H$ to be a free pro-$l$-group. We also obtain a description of all $\Gamma$-extensions $k_\infty/k$ having the property that any place of $k$ has a finite number of extensions to $k_\infty$. We prove that, in some sense, such $\Gamma$-extensions make up the overwhelming majority of all $\Gamma$-extensions.
Bibliography: 4 items.

Full text: PDF file (918 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Izvestiya, 1975, 9:3, 455–463

Bibliographic databases:

UDC: 519.4
MSC: Primary 12A60; Secondary 12G10, 12A55, 12A65, 12F10
Received: 18.06.1974

Citation: L. V. Kuz'min, “Cohomological dimension of some Galois groups”, Izv. Akad. Nauk SSSR Ser. Mat., 39:3 (1975), 487–495; Math. USSR-Izv., 9:3 (1975), 455–463

Citation in format AMSBIB
\Bibitem{Kuz75}
\by L.~V.~Kuz'min
\paper Cohomological dimension of some Galois groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1975
\vol 39
\issue 3
\pages 487--495
\mathnet{http://mi.mathnet.ru/izv2038}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=379437}
\zmath{https://zbmath.org/?q=an:0342.12008}
\transl
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 3
\pages 455--463
\crossref{https://doi.org/10.1070/IM1975v009n03ABEH001486}


Linking options:
  • http://mi.mathnet.ru/eng/izv2038
  • http://mi.mathnet.ru/eng/izv/v39/i3/p487

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. L. V. Kuz'min, “Local extensions associated with $l$-extensions with given ramification”, Math. USSR-Izv., 9:4 (1975), 693–726  mathnet  crossref  mathscinet  zmath
    2. V. A. Babaitsev, “On the linear nature of the behavior of Iwasawa's $\mu$ invariant”, Math. USSR-Izv., 19:1 (1982), 1–12  mathnet  crossref  mathscinet  zmath
    3. L. V. Kuz'min, “Some remarks on the $l$-adic Dirichlet theorem and the $l$-adic regulator”, Math. USSR-Izv., 19:3 (1982), 445–478  mathnet  crossref  mathscinet  zmath
    4. L. V. Kuz'min, “An analog of the Riemann–Hurwitz formula for one type of $l$-extensions of algebraic number fields”, Math. USSR-Izv., 36:2 (1991), 325–347  mathnet  crossref  mathscinet  zmath  adsnasa
    5. L. V. Kuz'min, “Some remarks on the $\ell$-adic regulator. IV”, Izv. Math., 64:2 (2000), 265–310  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. I. S. Rakhimov, “O povedenii arifmeticheskikh invariantov nekotorogo klassa ellipticheskikh krivykh v krugovykh $\Gamma$-rasshireniyakh”, Matem. tr., 8:1 (2005), 122–134  mathnet  mathscinet  zmath  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Number of views:
    This page:152
    Full text:53
    References:22
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019