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manuscripta mathematica

, Volume 43, Issue 1, pp 87–106 | Cite as

Global restrictions on ramification in number fields

  • H. Zantema
Article
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Abstract

Let G be the Galois group of a number field extension. For each primep a map ε(p)∶H2(G,{±1})→{±1} is defined. This local symbol has a global restriction: the product of ε(p) over all primes is trivial. This paper discusses how to compute ε(p) and gives an application to integer valued polynomials over certain quartic number fields.

Keywords

Number Theory Algebraic Geometry Topological Group Galois Group Number Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [CF]
    Cassels, J. W. S., and Fröhlich, A. (eds),Algebraic number theory, Academic Press, 1967.Google Scholar
  2. [F]
    Fröhlich, A.,Discriminants of algebraic number fields, Math. Zeitschr. 74 (1960), 18–28.Google Scholar
  3. [H]
    Huppert, B.,Endliche Gruppen I, Springer, 1967.Google Scholar
  4. [HS]
    Hall, M., and Senior, J. K.,The groups of order 2 n (n≤6), Macmillan New York, 1964.Google Scholar
  5. [P]
    Pólya, G.,Über ganzwertigen Polynome in algebraischen Zahl-körpern, J. Reine Angew. Math. 149 (1919), 97–116.Google Scholar
  6. [S1]
    Serre, J.-P.,Corps locaux, Hermann Paris, 1962.Google Scholar
  7. [S2]
    Serre, J.-P.,Cohomologie galoisienne, Lecture Notes in Mathematics 5, Springer, 1964.Google Scholar
  8. [S3]
    Serre, J.-P.,Structure de certains pro-p-groupes, Séminaire Bourbaki 252 (1963).Google Scholar
  9. [Sch]
    Schur, I.,Über die Darstellungen der symmetrischen und alternierenden Gruppen durch gebrochene lineare Substitutionen, J. Reine Angew. Math. 139 (1911), 155–250.Google Scholar
  10. [Z]
    Zantema, H.,Integer valued polynomials over a number field, Manuscripta math. 40 (1982), 155–203.Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • H. Zantema
    • 1
  1. 1.Department of MathematicsUniversiteit van AmsterdamAmsterdamThe Netherlands

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