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Proceedings of the American Mathematical Society

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
DOI: https://doi.org/10.1090/S0002-9939-1985-0806069-6
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?)

  • 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
  • J-P. Serre, Structure de certains pro-$p$ groupes, Séminaire Bourbaki 1962/63, exposé no. 252.
  • 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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Article copyright: © Copyright 1985 American Mathematical Society