A remark on the structure of absolute Galois groups
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- by Tilmann Würfel PDF
- Proc. Amer. Math. Soc. 95 (1985), 353-356 Request permission
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
- 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, Publications de l’Université de Nancago, No. VIII, Hermann, Paris, 1968 (French). Deuxième édition. MR 0354618
Additional Information
- © Copyright 1985 American Mathematical Society
- 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