Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Proceedings of the American Mathematical Society
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
MathSciNet review: 806069
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 (84i:12007)
  • [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 (50 #7096)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 12G05

Retrieve articles in all journals with MSC: 12G05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0806069-6
PII: S 0002-9939(1985)0806069-6
Article copyright: © Copyright 1985 American Mathematical Society



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia