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ISSN 1088-6826(online) ISSN 0002-9939(print)



A remark on the structure of absolute Galois groups

Author: Tilmann Würfel
Journal: Proc. Amer. Math. Soc. 95 (1985), 353-356
MSC: Primary 12G05
MathSciNet review: 806069
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Abstract: Let the field $ F$ contain all $ p$-power roots of unity for some prime $ p$ and suppose that the absolute Galois group $ G$ of $ F$ is a one-relator pro-$ p$ group. We use Merkurjev-Suslin's theorem on the power norm residue symbol to show that $ G$ is an extension of a Demushkin group by a free pro-$ p$ group.

References [Enhancements On Off] (What's this?)

  • [1] A. S. Merkur′ev and A. A. Suslin, 𝐾-cohomology of Severi-Brauer varieties and the norm residue homomorphism, Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), no. 5, 1011–1046, 1135–1136 (Russian). MR 675529
  • [2] J-P. Serre, Structure de certains pro-$ p$ groupes, Séminaire Bourbaki 1962/63, exposé no. 252.
  • [3] Jean-Pierre Serre, Corps locaux, Hermann, Paris, 1968 (French). Deuxième édition; Publications de l’Université de Nancago, No. VIII. MR 0354618

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