Trivialité du 2 -rang du noyau hilbertien

Hervé Thomas

Journal de théorie des nombres de Bordeaux (1994)

  • Volume: 6, Issue: 2, page 459-483
  • ISSN: 1246-7405


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 kernel and reveals existence of symbols on K not given by local class field theory.

How to cite


Thomas, Hervé. "Trivialité du $2$-rang du noyau hilbertien." Journal de théorie des nombres de Bordeaux 6.2 (1994): 459-483. <>.

author = {Thomas, Hervé},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {Milnor -group; Hilbert symbols; class field theory; biquadratic fields; Hilbert kernel; regular kernel},
language = {fre},
number = {2},
pages = {459-483},
publisher = {Université Bordeaux I},
title = {Trivialité du $2$-rang du noyau hilbertien},
url = {},
volume = {6},
year = {1994},

AU - Thomas, Hervé
TI - Trivialité du $2$-rang du noyau hilbertien
JO - Journal de théorie des nombres de Bordeaux
PY - 1994
PB - Université Bordeaux I
VL - 6
IS - 2
SP - 459
EP - 483
LA - fre
KW - Milnor -group; Hilbert symbols; class field theory; biquadratic fields; Hilbert kernel; regular kernel
UR -
ER -


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