1992-12-01
On the Galois module structure over CM-fields
Publication
Publication
Manuscripta Mathematica , Volume 75 - Issue 1 p. 333- 347
In this paper we make a contribution to the problem of the existence of a normal integral basis. Our main result is that unramified realizations of a given finite abelian group Δ as a Galois group Gal (N/K) of an extension N of a given CM-field K are invariant under the involution on the set of all realizations of Δ over K which is induced by complex conjugation on K and by inversion on Δ. We give various implications of this result. For example, we show that the tame realizations of a finite abelian group Δ of odd order over a totally real number field K are completely characterized by ramification and Galois module structure.
| Additional Metadata | |
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| doi.org/10.1007/BF02567089, hdl.handle.net/1765/15896 | |
| Manuscripta Mathematica | |
| Organisation | Erasmus School of Economics |
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Brinkhuis, J. (1992). On the Galois module structure over CM-fields. Manuscripta Mathematica, 75(1), 333–347. doi:10.1007/BF02567089
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