Geodesic
Abelian subgroups of Galois groups
Izvestiya. Mathematics, Tome 38 (1992) no. 1, pp. 27-67 
F. A. Bogomolov. Abelian subgroups of Galois groups. Izvestiya. Mathematics, Tome 38 (1992) no. 1, pp. 27-67. http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a1/
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     author = {F. A. Bogomolov},
     title = {Abelian subgroups of {Galois} groups},
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     year = {1992},
     volume = {38},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a1/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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]$.

[1] Bogomolov F. A., “Gruppa Brauera polei invariantov algebraicheskikh grupp”, Matem. sb., 180:2 (1989), 279–293 | MR | Zbl

[2] Bogomolov F. A., “Gruppa Brauera faktorprostranstv lineinykh predstavlenii”, Izv. AN SSSR. Ser. matem., 51:3 (1987), 485–516 | Zbl

[3] Merkurev A. S., Suslik A. A., “$K$-kogomologii mnogoobrazii Severi–Brauera i gomomorfizm normennogo vycheta”, Izv. AN SSSR. Ser. matem., 46:5 (1982), 1011–1061 | MR