Nous étudions, en tant que module galoisien, le groupe des unités des extensions biquadratiques de corps de nombres . Le -rang du premier groupe de cohomologie des unités de est calculé pour quelconque. Pour quadratique imaginaire, nous déterminons la plupart des cas (incluant le cas non ramifiée) où l’indice prend sa valeur maximale , avec les unités modulo la torsion de et les unités modulo la torsion d’un des trois sous-corps quadratiques de .
We investigate as Galois module the unit group of biquadratic extensions of number fields. The -rank of the first cohomology group of units of is computed for general . For imaginary quadratic we determine a large portion of the cases (including all unramified ) where the index takes its maximum value , where are units mod torsion of and are units mod torsion of one of the 3 quadratic subfields of .
@article{JTNB_2008__20_1_183_0, author = {Marcin Mazur and Stephen V. Ullom}, title = {Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {183--204}, publisher = {Universit\'e Bordeaux 1}, volume = {20}, number = {1}, year = {2008}, doi = {10.5802/jtnb.621}, mrnumber = {2434163}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.621/} }
TY - JOUR AU - Marcin Mazur AU - Stephen V. Ullom TI - Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields JO - Journal de théorie des nombres de Bordeaux PY - 2008 SP - 183 EP - 204 VL - 20 IS - 1 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.621/ DO - 10.5802/jtnb.621 LA - en ID - JTNB_2008__20_1_183_0 ER -
%0 Journal Article %A Marcin Mazur %A Stephen V. Ullom %T Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields %J Journal de théorie des nombres de Bordeaux %D 2008 %P 183-204 %V 20 %N 1 %I Université Bordeaux 1 %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.621/ %R 10.5802/jtnb.621 %G en %F JTNB_2008__20_1_183_0
Marcin Mazur; Stephen V. Ullom. Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields. Journal de théorie des nombres de Bordeaux, Tome 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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