Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields
Journal de Théorie des Nombres de Bordeaux, Volume 20 (2008) no. 1, pp. 183-204.

We investigate as Galois module the unit group of biquadratic extensions L/M of number fields. The 2-rank of the first cohomology group of units of L/M is computed for general M. For M imaginary quadratic we determine a large portion of the cases (including all unramified L/M) where the index [V:V 1 V 2 V 3 ] takes its maximum value 8, where V are units mod torsion of L and V i are units mod torsion of one of the 3 quadratic subfields of L/M.

Nous étudions, en tant que module galoisien, le groupe des unités des extensions biquadratiques de corps de nombres L/M. Le 2-rang du premier groupe de cohomologie des unités de L/M est calculé pour M quelconque. Pour M quadratique imaginaire, nous déterminons la plupart des cas (incluant le cas L/M non ramifiée) où l’indice [V:V 1 V 2 V 3 ] prend sa valeur maximale 8, avec V les unités modulo la torsion de L et V i les unités modulo la torsion d’un des trois sous-corps quadratiques de L/M.

Received:
Published online:
DOI: 10.5802/jtnb.621
Marcin Mazur 1; Stephen V. Ullom 2

1 Department of Mathematics Binghamton University P.O. Box 6000 Binghamton, NY 13892-6000
2 Department of Mathematics University of Illinois at Urbana-Champaign 1409 W. Green Street Urbana, Illinois 61801-2975
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Marcin Mazur; Stephen V. Ullom. Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields. Journal de Théorie des Nombres de Bordeaux, Volume 20 (2008) no. 1, pp. 183-204. doi : 10.5802/jtnb.621. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.621/

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