Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-26T08:55:18.698Z Has data issue: false hasContentIssue false
  • English
  • Français

Resolvents and trace form

Published online by Cambridge University Press:  24 October 2008

A. Fröhlich
A. Fröhlich
Affiliation:
King's College, University of London
Get access Rights & Permissions [Opens in a new window]

Extract

This paper is a continuation of (F3). In its first part we shall expand and extend the general theory of the earlier paper, while in the second part we specialize to number fields. The theory of resolvents and of the trace form, presented here, complements the more arithmetic theory of module conductors and module resolvents as described elsewhere (cf. (F4)). Both these papers will be applied in work on the connexion, for tame extensions, between Galois module structure of algebraic integers on the one hand, and Artin conductors and root numbers on the other hand (cf. (F5)). The results of the present paper are however not restricted to the tame case and, it is hoped, will subsequently be applied in a more general context.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 2 , September 1975 , pp. 185 - 210
Copyright
Copyright © Cambridge Philosophical Society 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(D)Deligne, P.Les constantes des équations fonctionelles des functions L, Modular Functions in one variable II, Springer Lecture Notes, 349 (1973), 501–597.Google Scholar
(F1)Fröhlich, A.Discriminants of algebraic number fields. Math. Z. 74 (1960), 18–28.Google Scholar
(F2)Fröhlich, A.Ideals in an extension field as modules over the algebraic integers in a finite number field. Math. Z. 74 (1960), 29–38.CrossRefGoogle Scholar
(F3)Fröhlich, A.Resolvents, discriminants and trace invariants. Journ. of Alg. 4 (1966), 173–198.CrossRefGoogle Scholar
(F4)Fröhlich, A. Module conductors and module resolvents (to appear in Proc. London Math. Soc.)Google Scholar
(F5)Fröhlich, A. Arithmetic and Galois module structure for tame extensions (to be published).Google Scholar
(F6)Fröhlich, A.Artin rootnumbers, conductors and representations for generalised quaternion groups. Proc. London Math. Soc. 28 (1974), 402–438.CrossRefGoogle Scholar
(FM)Fröhlich, A. and McEvett, A. M.The representations of groups by automorphisms of forms. J. Alg. 12 (1969), 114–133.CrossRefGoogle Scholar
(H)Masse, H., Artinsche Führer, Artinsche L-Funktionen und Gaussche Summen über endlich algebraischen Zahlkörpern. Acta Salmanticensia, 1954.Google Scholar
(T)Taussky, O.The discriminant matrix of a number field. J. London Math. Soc. 43 (1968), 152–154.CrossRefGoogle Scholar
(W)Wall, C. T. C.On the classification of Hermitian forms. IV. Adele rings. Invent Math. 23 (1974), 241–260.Google Scholar