Hostname: page-component-7dd5485656-k8lnt Total loading time: 0 Render date: 2025-10-31T14:38:40.359Z Has data issue: false hasContentIssue false
  • English
  • Français

Extensions of number fields defined by cohomology groups

Published online by Cambridge University Press:  22 January 2016

Hans Opolka
Hans Opolka*
Affiliation:
Mathematisches Institut, Einsteinstrasse 64, D-4400 Münster
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let k be a field of characteristic 0, let be an algebraic closure of k and denote by Gk = G(/k) the absolute Galois group of k. Suppose that for some natural number n ≥ 3 the cohomology group Hn(Gk) Z) is trivial.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 92 , December 1983 , pp. 179 - 186
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1983

References

[1] Artin, E. and Tate, J., Class Field Theory, Benjamin, New York, 1967.Google Scholar
[2] Cassels, J.W.S. and Fröhlich, A., Algebraic number theory, Academic Press, New York, 1967.Google Scholar
[3] Fröhlich, A., On fields of class two, Proc. London Math. Soc., 4 (1954), 235–256.Google Scholar
[4] Masuda, K., An application of the generalized norm residue symbol, Proc. Amer. Math. Soc., 10 (1959), 245–252.Google Scholar
[5] Miyake, K., On the structure of the idele groups of algebraic number fields II, Tohoku Math. J., 34 (1982), 101–112.Google Scholar
[6] Opolka, H., Zur Auflösung zahlentheoretischer Knoten, Math. Z., 173 (1980), 95–103.Google Scholar
[7] Razar, M. J., Central and genus class fields and the Hasse norm theorem, Composito Math., 35 (1977), 281–298.Google Scholar
[8] Scholz, A., Totale Normenreste, die keine Normen sind, als Erzeuger nichtabelscher Körpererweiterungen II, J. Reine Angew. Math., 182 (1940), 217–234.Google Scholar
[9] Serre, J. P., Cohomologie Galoisienne, Lecture Notes in Math., 5 Springer (1965).Google Scholar
[10] Serre, J. P., Modular forms of weight one and Galois representations, in: Algebraic number fields (ed. Fröhlich, A.), Durham Symposium, Academic Press, London, 1977.Google Scholar
[11] Shatz, S., Profinite groups, arithmetic and geometry, Princeton University Press, 1972.Google Scholar
[12] Shirai, S., On the central class field mood m of Galois extensions of an algebraic number field, Nagoya Math. J., 71 (1978), 61–85.Google Scholar
[13] Miyake, K., On central extensions of a Galois extension of algebraic number fields, Manuscript, 1982.Google Scholar