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Trivialité du 2 -rang du noyau hilbertien

Hervé Thomas — 1994

Journal de théorie des nombres de Bordeaux

We give exhaustive list of biquadratic fields K = ( i , m ) and K = ( 2 , m ) without 2 -exotic symbol, i.e. for which the 2 -rank of the Hilbert kernel (or wild kernel) is zero. Such K = ( i , m ) are logarithmic principals [J3]. We detail an exemple of this technical numerical exploration and quote the family of theories and results we utilize. The 2 -rank of tame, regular and wild kernel of K -theory are connected with local and global problem of embedding in a Z 2 -extension. Global class field theory can describe the 2 -rank of the Hilbert...

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