Keywords
- Number Field
- Maximal Order
- Galois Extension
- Grothendieck Group
- Abelian Extension
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References
J.V. Armitage, Zeta functions with zero at s=1/2, Inv. Math. 15 (1972), 199–205.
A.-M. Bergé, Projectivité des anneaux d’entiers sur leurs ordres associés. In Thèse d’état, Bordeaux, 1979.
J. Brinkhuis, Normal integral bases and embedding problems, Math. Ann. 264 (1983), 537–543.
J. Brinkhuis, Galois modules and embedding problems, J. reine angew. Math., 346, 1984, 141–165.
Ph. Cassou-Noguès, M.J. Taylor, Local rootnumbers and Hermitian-Galois module structure of rings of integers, Math. Annalen. 263, 251–261, 1983.
Ph. Cassou-Noguès, M.J. Taylor, Constante de l’equation fonctionelle de la fonction L d’Artin d’une représentation symplectique et modéreé, Ann. Inst. Fourier, 1983, XXXIII (2).
J. Cougnard, Un contreexemple à une conjecture de J. Martinet, in "Algebraic Number fields", Proc. Durham Symp., 1977, Academic Press.
J. Cougnard, Propriétés galoisiennes des anneaux d’entiers des p-extensions, Compositio Math., 33 (1976), 303/336.
A. Fröhlich, Invariants for modules over commutative separable orders, Quart. J. Math. Oxford, (2), 16, 1965, 193–232.
A. Fröhlich, Galois module structure of algebraic integers, Ergebnisse (3) 1, Springer-Verlag, 1983.
A. Fröhlich, Value distributions of symplectic root numbers, Proc. L.M.S.
A. Fröhlich, Classgroups and Hermitian modules, Birkhauser.
A. Fröhlich, Discriminants of algebraic number fields, Math. Zeit. 74 (1960), 18–28.
A. Fröhlich, The module structure of Kummer extensions over Dedekind domains, Crelle, 209 (1962), 39–53.
A. Fröhlich, Arithmetic and Galois module structure for tame extensions, J. reine angew. Math. 286/287, 1976, 380–440.
A. Fröhlich, Some problems of Galois module structure for wild extensions, Proc. L.M.S. (3) 37, 1978, 193–212.
A. Fröhlich, Gauss’che Summen, printed notes, Math. Institut, Univ. Köln, 1983.
R. Fueter, Vorlesungen über die singulären Möduln und die Komplexe Multiplikation der elliptischen Funktionen, 1 und 2, Leipzig-Berlin, 1924.
A. Fröhlich, J. Queyrut, On the functional equation of the Artin L-function for characters of real representations, Inv. Math. 20 (1973), 125–138.
F. Kawamoto, On normal integral bases, preprint.
H.W. Leopoldt, Über die Hauptordnung der ganzen Elemente eines abelschen Zahlkörpers, Crelle 201 (1959), 119–149.
B. Martel, Sur l’anneau des entiers d’une extension biquadratique d’un corps 2-adique, C.R.A.S. Paris t 278, 1974.
J. Martinet, Character theory and Artin L-functions, in "Algebraic Number Fields", Proc. Durham Symp., Academic Press, 1977.
L. McCulloh, Galois module structure of elementary abelian extensions, to appear in J. Alg.
E. Noether, Normalbasis bei Körpern ohne höhere Verzweigung, Crelle 167 (1932), 147–152.
J. Queyrut, S-groupes des classes d’un ordre arithmétique, J. Alg. 76 (1982), 234–260.
J. Queyrut, Structure galoisienne des anneaux d’entiers d’extensions sauvagement ramifiées, Ann. Inst. Fourier, 31 (3), 1981, 1–35.
M.J. Taylor, Classgroups of group rings, L.M.S. Lecture Notes Series 91, Cam. Univ. Press. 1984.
M.J. Taylor, On Fröhlich’s conjecture for rings of integers of tame extensions, Inv. Math., 63 (1981), 41–79.
M.J. Taylor, On the self-duality of rings of integers as a Galois module, Inv. Math., 46 (1978), 173–177.
M J. Taylor, Galois module structure of rings of integers of Kummer extensions, Bull. L.M.S. 12 (1980), 96–98.
M.J. Taylor, Formal groups and the Galois module structure of local rings of integers, to appear.
M.J. Taylor, Relative Galois module structure of rings of integers and elliptic functions II, to appear in Annals of Math.
M.J. Taylor, Relative Galois module structure of rings of integers and elliptic functions III, to appear.
M.J. Taylor, Galois module structure of integers of relative abelian extensions, Crelle 303/4, 1978, 97–101.
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© 1985 Springer-Verlag
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Taylor, M.J. (1985). Relative galois module structure of rings of integers. In: Reiner, I., Roggenkamp, K.W. (eds) Orders and their Applications. Lecture Notes in Mathematics, vol 1142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074807
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DOI: https://doi.org/10.1007/BFb0074807
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