Structure galoisienne et ramification sauvage. (Galois structure and wild ramification). (French) Zbl 0682.12004

Sémin. Théor. Nombres, Univ. Bordeaux I 1987-1988, Exp. No. 46, 8 p. (1988).
This note, without proofs, concerns the generalization to wild extensions of the Galois module structure theory for finite tame extensions of number fields, a survey of which is the matter of A. Fröhlich’s book “Galois module structure of algebraic integers” (1983; Zbl 0501.12012).
Here, the author propounds a conjecture which generalizes the Fröhlich- Taylor’s result connecting the Galois module structure of a tame Galois extension, with group \(\Gamma\), to the sign of the constant in the Artin L-function associated to a symplectic character of \(\Gamma\). The proof of this conjecture in a particular case is announced in a forthcoming paper by the author.
Reviewer: R.Massy


11R32 Galois theory
11R52 Quaternion and other division algebras: arithmetic, zeta functions
11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers


Zbl 0501.12012
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