Displaying similar documents to “Hasse’s problem for monogenic fields”

Unit indices and cohomology for biquadratic extensions of imaginary quadratic fields

Marcin Mazur, Stephen 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 .