Trivialité du 2-rang du noyau hilbertien
Journal de théorie des nombres de Bordeaux, Tome 6 (1994) no. 2, pp. 459-483.

We give exhaustive list of biquadratic fields K=ℚ(i,m) and K=ℚ(2,m) without 2-exotic symbol, i.e. for which the 2-rank of the Hilbert kernel (or wild kernel) is zero. Such K=ℚ(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.

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     author = {Herv\'e Thomas},
     title = {Trivialit\'e du $2$-rang du noyau hilbertien},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {459--483},
     publisher = {Universit\'e Bordeaux I},
     volume = {6},
     number = {2},
     year = {1994},
     zbl = {0822.11079},
     mrnumber = {1360655},
     language = {fr},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_1994__6_2_459_0/}
}
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Hervé Thomas. Trivialité du $2$-rang du noyau hilbertien. Journal de théorie des nombres de Bordeaux, Tome 6 (1994) no. 2, pp. 459-483. https://jtnb.centre-mersenne.org/item/JTNB_1994__6_2_459_0/

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