Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields

@article{Mazur2008UnitIA,
  title={Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields},
  author={Marcin Mazur and Stephen V. Ullom},
  journal={Journal de Theorie des Nombres de Bordeaux},
  year={2008},
  volume={20},
  pages={183-204}
}
  • M. Mazur, S. Ullom
  • Published 2008
  • Mathematics
  • Journal de Theorie des Nombres de Bordeaux
Nous etudions, en tant que module galoisien, le groupe des unites des extensions biquadratiques de corps de nombres L/M. Le 2-rang du premier groupe de cohomologie des unites de L/M est calcule pour M quelconque. Pour M quadratique imaginaire, nous determinons la plupart des cas (incluant le cas L/M non ramifiee) ou l'indice |V: V 1 V 2 V 3 ] prend sa valeur maximale 8, avec V les unites modulo la torsion de L et V i les unites modulo la torsion d'un des trois sous-corps quadratiques de L/M. 
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E-mail : mazur@math.binghamton.edu Stephen V. Ullom Department of Mathematics University of Illinois at Urbana-Champaign 1409 W
  • E-mail : mazur@math.binghamton.edu Stephen V. Ullom Department of Mathematics University of Illinois at Urbana-Champaign 1409 W
E-mail : ullom@math.uiuc.edu Manuscrit reçu le 31 janvier
  • E-mail : ullom@math.uiuc.edu Manuscrit reçu le 31 janvier
  • 2007