Normal integral bases and the Spiegelungssatz of Scholz

Jan Brinkhuis

Acta Arithmetica (1995)

  • Volume: 69, Issue: 1, page 1-9
  • ISSN: 0065-1036

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Jan Brinkhuis. "Normal integral bases and the Spiegelungssatz of Scholz." Acta Arithmetica 69.1 (1995): 1-9. <http://eudml.org/doc/206669>.

@article{JanBrinkhuis1995,
author = {Jan Brinkhuis},
journal = {Acta Arithmetica},
keywords = {normal integral bases; Spiegelungssatz; unramified cyclic cubic extensions; 3-class group; Scholz mirror},
language = {eng},
number = {1},
pages = {1-9},
title = {Normal integral bases and the Spiegelungssatz of Scholz},
url = {http://eudml.org/doc/206669},
volume = {69},
year = {1995},
}

TY - JOUR
AU - Jan Brinkhuis
TI - Normal integral bases and the Spiegelungssatz of Scholz
JO - Acta Arithmetica
PY - 1995
VL - 69
IS - 1
SP - 1
EP - 9
LA - eng
KW - normal integral bases; Spiegelungssatz; unramified cyclic cubic extensions; 3-class group; Scholz mirror
UR - http://eudml.org/doc/206669
ER -

References

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  1. [B1] J. Brinkhuis, Normal integral bases and complex conjugation, J. Reine Angew. Math. 375/376 (1987), 157-166. Zbl0609.12009
  2. [B2] J. Brinkhuis, Galois module structure as the obstruction to a local-global principle, J. Algebra 145 (1992), 454-462. Zbl0745.11052
  3. [B3] J. Brinkhuis, On the Galois module structure over CM-fields, Manuscripta Math. 75 (1992), 333-347. Zbl0757.11044
  4. [C-F] J. W. S. Cassels and A. Fröhlich, Algebraic Number Theory, Academic Press, London, 1967. Zbl0153.07403
  5. [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. Zbl0733.11044
  6. [C-T] Ph. Cassou-Noguès and M. J. Taylor, Elliptic Functions and Rings of Integers, Progr. Math. 66, Birkhäuser, Boston, 1987. Zbl0621.12012
  7. [F] A. Fröhlich, Galois Module Structure of Algebraic Integers, Ergeb. Math. Grenzgeb. (3) 1, Springer, 1981. Zbl0501.12012
  8. [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. 
  9. [Jac] N. Jacobson, Lectures in Algebra, Vol. III, Princeton Univ. Press, 1964. 
  10. [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. 
  11. [S] A. Scholz, Über die Beziehung der Klassenzahlen quadratischer Körper zueinander, J. Reine Angew. Math. 166 (1932), 201-203. Zbl0004.05104
  12. [T1] M. J. Taylor, On Fröhlich's conjecture for rings of integers of tame extensions, Invent. Math. 63 (1981), 41-79. Zbl0469.12003
  13. [T2] M. J. Taylor, Relative Galois module structure of rings of integers and elliptic functions II, Ann. of Math. 121 (1985), 519-535. Zbl0594.12008
  14. [T3] M. J. Taylor, Rings of integers and trace forms for tame extensions of odd degree, Math. Z. 202 (1989), 313-341. Zbl0723.11055
  15. [T4] M. J. Taylor, The Galois module structure of certain arithmetic principal homogeneous spaces, J. Algebra 153 (1992), 203-214. Zbl0776.11065

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