Normal integral bases and the Spiegelungssatz of Scholz

• Autorzy: Jan Brinkhuis
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 69
• Numer: 1
• Strony: 1-9

Daty

wydano

1995

otrzymano

1991-02-08

poprawiono

1992-07-20

Twórcy

autor

Jan Brinkhuis

• Econometric Institute, Erasmus University, P.O. Box 1738, 3000 DR Rotterdam, The Netherlands

Bibliografia

• [B1] J. Brinkhuis, Normal integral bases and complex conjugation, J. Reine Angew. Math. 375/376 (1987), 157-166.
• [B2] J. Brinkhuis, Galois module structure as the obstruction to a local-global principle, J. Algebra 145 (1992), 454-462.
• [B3] J. Brinkhuis, On the Galois module structure over CM-fields, Manuscripta Math. 75 (1992), 333-347.
• [C-F] J. W. S. Cassels and A. Fröhlich, Algebraic Number Theory, Academic Press, London, 1967.
• [Ca-Ch-F-T] Ph. Cassou-Noguès, T. Chinburg, A. Fröhlich and M. J. Taylor, L-functions and Galois modules, Notes by D. Burns and N. P. Byott, in: Proceedings of the Durham Symposium, July 1989, Cambridge University Press, Cambridge, 1991, 75-139.
• [C-T] Ph. Cassou-Noguès and M. J. Taylor, Elliptic Functions and Rings of Integers, Progr. Math. 66, Birkhäuser, Boston, 1987.
• [F] A. Fröhlich, Galois Module Structure of Algebraic Integers, Ergeb. Math. Grenzgeb. (3) 1, Springer, 1981.
• [H] D. Hilbert, Die Theorie der algebraischen Zahlkörper ('Zahlbericht'), Jahresber. Deutsch. Math.-Verein. 4 (1897), 175-546, or: Gesammelte Abhandlungen , I, Berlin, 1932, 63-363.
• [Jac] N. Jacobson, Lectures in Algebra, Vol. III, Princeton Univ. Press, 1964.
• [Jau] J.-F. Jaulent, Dualité dans les corps surcirculaires, in: Séminaire de Théorie des Nombres, Paris 1986-87, Progr. Math. 75, Birkhäuser, 1988, 183-220.
• [S] A. Scholz, Über die Beziehung der Klassenzahlen quadratischer Körper zueinander, J. Reine Angew. Math. 166 (1932), 201-203.
• [T1] M. J. Taylor, On Fröhlich's conjecture for rings of integers of tame extensions, Invent. Math. 63 (1981), 41-79.
• [T2] M. J. Taylor, Relative Galois module structure of rings of integers and elliptic functions II, Ann. of Math. 121 (1985), 519-535.
• [T3] M. J. Taylor, Rings of integers and trace forms for tame extensions of odd degree, Math. Z. 202 (1989), 313-341.
• [T4] M. J. Taylor, The Galois module structure of certain arithmetic principal homogeneous spaces, J. Algebra 153 (1992), 203-214.