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Izv. Akad. Nauk SSSR Ser. Mat., 1991, Volume 55, Issue 1, Pages 32–67 (Mi izv1021)  

This article is cited in 5 scientific papers (total in 5 papers)

Abelian subgroups of Galois groups

F. A. Bogomolov


Abstract: The author proves that every Abelian subgroup of rank $>1$ in the Galois group $G=\operatorname{Gal}(\overline K/K)$ of the algebraic closure of a rational function field $K$ is contained in a ramification subgroup, and also that the unramified Brauer group $\operatorname{Br}_vK$ equals the unramified Brauer group $\operatorname{Br}_v(G^c)$ defined in [2], §3, where $G^c$ is the quotient group $ G^c= G/[[G,G],G]$.

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English version:
Mathematics of the USSR-Izvestiya, 1992, 38:1, 27–67

Bibliographic databases:

UDC: 512.76+512.664.4
MSC: Primary 12F10; Secondary 13A20, 19C30, 51A99
Received: 01.11.1989

Citation: F. A. Bogomolov, “Abelian subgroups of Galois groups”, Izv. Akad. Nauk SSSR Ser. Mat., 55:1 (1991), 32–67; Math. USSR-Izv., 38:1 (1992), 27–67

Citation in format AMSBIB
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\by F.~A.~Bogomolov
\paper Abelian subgroups of Galois groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1991
\vol 55
\issue 1
\pages 32--67
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\adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?1992IzMat..38...27B}
\transl
\jour Math. USSR-Izv.
\yr 1992
\vol 38
\issue 1
\pages 27--67
\crossref{https://doi.org/10.1070/IM1992v038n01ABEH002186}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1992HG30700002}


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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. F. A. Bogomolov, “Stable cohomology of groups and algebraic varieties”, Russian Acad. Sci. Sb. Math., 76:1 (1993), 1–21  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    2. M. Z. Rovinskii, “Automorphism groups of fields, and their representations”, Russian Math. Surveys, 62:6 (2007), 1121–1186  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Sunil K. Chebolu, Ido Efrat, Ján Mináč, “Quotients of absolute Galois groups which determine the entire Galois cohomology”, Math. Ann, 2011  crossref
    4. Fedor Bogomolov, Yuri Tschinkel, “Reconstruction of higher-dimensional function fields”, Mosc. Math. J., 11:2 (2011), 185–204  mathnet  mathscinet
    5. Ido Efrat, “The Zassenhaus filtration, Massey products, and representations of profinite groups”, Advances in Mathematics, 263 (2014), 389  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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