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Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields

Marcin MazurStephen V. Ullom — 2008

Journal de Théorie des Nombres de Bordeaux

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 .

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