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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cassels, J. W. S., and Fröhlich, A. (eds),Algebraic number theory, Academic Press, 1967.
Fröhlich, A.,Discriminants of algebraic number fields, Math. Zeitschr. 74 (1960), 18–28.
Huppert, B.,Endliche Gruppen I, Springer, 1967.
Hall, M., and Senior, J. K.,The groups of order 2 n (n≤6), Macmillan New York, 1964.
Pólya, G.,Über ganzwertigen Polynome in algebraischen Zahl-körpern, J. Reine Angew. Math. 149 (1919), 97–116.
Serre, J.-P.,Corps locaux, Hermann Paris, 1962.
Serre, J.-P.,Cohomologie galoisienne, Lecture Notes in Mathematics 5, Springer, 1964.
Serre, J.-P.,Structure de certains pro-p-groupes, Séminaire Bourbaki 252 (1963).
Schur, I.,Über die Darstellungen der symmetrischen und alternierenden Gruppen durch gebrochene lineare Substitutionen, J. Reine Angew. Math. 139 (1911), 155–250.
Zantema, H.,Integer valued polynomials over a number field, Manuscripta math. 40 (1982), 155–203.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zantema, H. Global restrictions on ramification in number fields. Manuscripta Math 43, 87–106 (1983). https://doi.org/10.1007/BF01169099
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01169099