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On the Galois structure of the square root of the codifferent. (English) Zbl 0727.11047
Let \({\mathcal O}_ L\) be the maximal order in a finite abelian extension \(L\) of \(\mathbb Q\). In the case where there exists a (unique) fractional \({\mathcal O}_ L\)-ideal, (which is unimodular with respect to the trace form of \(L/\mathbb Q)\), the authors investigate its Galois structure.

MSC:
11R32 Galois theory
13B05 Galois theory and commutative ring extensions
11R33 Integral representations related to algebraic numbers; Galois module structure of rings of integers
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References:
[1] Bachoc, C., Sur les réseaux unimodulaires pour la forme Trace(x2), Proceedings of the Séminaire de Théorie des Nombres de Paris (1988-1989). · Zbl 0734.11029
[2] Bachoc, C., Sur la structure hermitienne de la racine carrée de la codifférente, to appear. · Zbl 0789.11062
[3] Bachoc, C. et Erez, B., Forme trace et ramification sauvage, Proc. London Math. Soc.61 (1990), 209-226. · Zbl 0708.11059
[4] Bergé, A-M., Arithmétique d’une extension galoisienne à groupe d’inertie cyclique, Ann. Inst. Fourier28 (1978), 17-44. · Zbl 0377.12009
[5] Bergé, A-M., A propos du genre des entiers d’une extension, Publications Math. Sc. Besançon (1979- 1980), 1-9. · Zbl 0472.12006
[6] Burns, D., Canonical factorisability and a variant of Martinet’s conjecture, to appear in J. London Math. Soc. (1991). · Zbl 0751.11053
[7] Erez, B., Structure galoasienne et forme trace, Thèse, Genève1987; see also J. Algebra118 (1988), 438-446. · Zbl 0663.12015
[8] Erez, B., A survey of recent work on the square root of the inverse different, to appear in the proceedings of the Journées arithmétiques, Luminy (1989). · Zbl 0752.11048
[9] Erez, B. and Taylor, M.J., Hermitian modules in Galois extensions of number fields and Adams operations, to appear. · Zbl 0756.11035
[10] Fröhlich, A., Galois module structure of algebraic integers, Ergebnisse der Mathematik 3. Folge, Bd. 1Berlin: Springer (1983). · Zbl 0501.12012
[11] Lang, S., Algebraic Number Theory, Springer-Verlag, Heidelberg (1986). · Zbl 0601.12001
[12] Leopoldt, H.W., Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, J. reine und angew. Math201 (1959), 119-149. · Zbl 0098.03403
[13] Lettl, G., The ring of integers of an abelian number field, J. reine und angew. Math.400 (1990), 162-170. · Zbl 0703.11060
[14] Reiner, I., Maximal Orders, Academic Press, London (1975). · Zbl 0305.16001
[15] Serre, J-P., Corps Locaux, Hermann, Paris, (1962).
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