A survey of recent work on the square root of the inverse different

Erez, Boas

Journées arithmétiques de Luminy 17-21 Juillet 1989, Astérisque, no. 198-199-200 (1991), pp. 133-152

MR Zbl | 4 citations dans Numdam

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     author = {Erez, Boas},
     title = {A survey of recent work on the square root of the inverse different},
     booktitle = {Journ\'ees arithm\'etiques de Luminy 17-21 Juillet 1989},
     editor = {Lachaud Gilles},
     series = {Ast\'erisque},
     pages = {133--152},
     year = {1991},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {198-199-200},
     mrnumber = {1144319},
     zbl = {0752.11048},
     language = {en},
     url = {https://www.numdam.org/item/AST_1991__198-199-200__133_0/}
}

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Erez, Boas. A survey of recent work on the square root of the inverse different, dans Journées arithmétiques de Luminy 17-21 Juillet 1989, Astérisque, no. 198-199-200 (1991), pp. 133-152. https://www.numdam.org/item/AST_1991__198-199-200__133_0/

Bibliographie
Cité par

[Ba] Bachoc C., Sur les réseaux unimodulaires pour la forme Trace $(x^{2})$ , to appear in the proceedings of the Séminaire de Théorie des Nombres de Paris, (1988-1989). | MR | Zbl

[B-E] Bachoc C., Erez B., Forme trace et ramification sauvage, Proc. London Math. Soc. (3) 61 (1990), 209-226. | MR | Zbl | DOI

[Bas] Bass H., Unitary algebraic $K$ -theory, 57-265, in Algebraic $K$ -theory III, Proceedings of Batelle Institute Conference (1972), Springer Lecture Notes 343, Berlin, Springer (1973). | Zbl | MR

[B-L] Bayer E., Lenstra H. W., Forms in odd degree extensions and self-dual normal bases, American J. of Math., 112 (1990), 359-373. | MR | Zbl | DOI

[Be] Bergé A.-M., Extensions galoisiennes a groupe d'inertie cyclique, Ann. Inst. Fourier, 28 (1978), 17-44. | MR | Zbl | EuDML | Numdam | DOI

[Bu1] Burns D., Factorisability, group lattices and Galois module structure, J. of Algebra, 134 (1990), 257-270. | MR | Zbl | DOI

[Bu2] Burns D., Factorisability and wildly ramified Galois extensions, to appear in Ann. Inst. Fourier. | MR | Zbl | EuDML | Numdam

[Bu3] Burns D., Canonical factorisability and a variant of Martinet's conjecture, to appear in J. of the London Math. Soc.. | MR | Zbl

[C] Cohn H., A classical invitation to algebraic numbers and class fields, Universitext. New-York, Springer (1978). | MR | Zbl

[CN-T] Cassou-Noguès Ph., Taylor M. J., Opérations d'Adams et groupes de classes d'algèbre de groupe, J. of Algebra (1), 95 (1985), 125-152. | MR | Zbl | DOI

[C-P] Conner P., Perlis R., A survey of trace forms in algebraic number fields, Singapore, World Scientific (1984). | MR | Zbl

[C-R] Curtis C., Reiner I., Methods of representation theory, 2 volumes, New-York, John Wiley and Sons (1981-1987). | MR | Zbl

[E1] Erez B., The Galois structure of the trace form in extensions of odd prime degree, J. of Algebra, 118 (1988), 438-446. | MR | Zbl | DOI

[E2] Erez B., The Galois structure of the square root of the inverse different, to appear in Math. Z.. | MR | Zbl | EuDML

[E3] Erez B., Structure galoisienne et forme trace, Genève, Thèse (1987). | Zbl

[E-M] Erez B., Morales J., The hermitian structure of rings of integers in odd degree abelian extensions, to appear in J. of Number Theory. | MR | Zbl

[E-T] Erez B., Taylor M. J., Hermitian modules in Galois extensions of number fields and Adams operations, Preprint (1990). | MR | Zbl

[F1] Fröhlich A., Galois module structure of algebraic integers, Ergebnisse der Mathematik, 3, Folge, Bd. 1, Berlin, Springer (1983). | MR | Zbl

[F2] Fröhlich A., Invariants for modules over commutative separable orders, Quart. J. Math. Oxford, 16 (1965), 193-232. | MR | Zbl | DOI

[F3] Fröhlich A., $L$ -values at zero and multiplicative Galois module structure (also Galois-Gauss sums and additive Galois module structure), J. Reine und Angew. Math., 397 (1989), 42-99. | MR | Zbl | EuDML

[K] Kervaire M., Opérations d'Adams en théorie des représentations linéaires des groupes finis, l'Ens. Math., T. XXII, 1-28 (1976). | MR | Zbl

[L] Leopoldt H. W., Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, J. Reine und Angew, Math., 201 (1959), 119-149. | MR | Zbl | EuDML

[Ma] Martinet J., Character theory and Artin $L$ -functions, 1-87, in Algebraic Number Fields, Proceedings of the Durham Symposium 1975, London, Academic Press (1977). | MR | Zbl

[Mil] Miyata Y., Vertices of ideals of a $p$ -adic number field, Illinois J. of Math. (2), 31 (1987), 185-199. | MR | Zbl

[Mi2] Miyata Y., Vertices of ideals of a $p$ -adic number field II, Nagoya Math. J., 107, 49-62 (1987). | MR | Zbl | DOI

[S1] Serre J.-P., Corps locaux, 3rd edition, Paris, Hermann (1968). | MR

[T1] Taylor M. J., Rings of integers and trace forms, Math. Z, 202, 313-341 (1989). | MR | Zbl | EuDML | DOI

[T2] Taylor M. J., Classgroups of group rings, London Mathematical SocietyLecture Note Series 91, Cambridge, Cambridge University Press (1984). | MR | Zbl

[U1] Ullom S., Normal bases in Galois extensions of number fields, Nagoya Math. J., 34, 153-167. | MR | Zbl | DOI

[U2] Ullom S., Galois cohomology of ambiguous ideals, J. Number Th., 1, 11-15 (1969). | MR | Zbl | DOI