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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
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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