In the previous paper [15], we determined the structure of the Galois groups of the maximal unramified extensions of imaginary quadratic number fields of conductors under the Generalized Riemann Hypothesis (GRH) except for 23 fields (these are of conductors ) and give a table of . We update the table (under GRH). For 19 exceptional fields of them, we determine . In particular, for , we obtain , the fourth Hilbert class field of . This is the first example of a number field whose class field tower has length four.
Dans l’article [15], nous donnions dans une table la structure des groupes de Galois des extensions maximales non ramifiées des corps de nombres quadratiques imaginaires de conducteur sous l’Hypothèse de Riemann Généralisée, sauf pour 23 d’entre eux (tous de conducteur ). Ici nous mettons à jour cette table, en précisant, pour 19 de ces corps exceptionnels, la structure de . En particulier pour , nous obtenons , le quatrième corps de classes de Hilbert de . C’est le premier exemple d’un corps de nombres dont la tour de corps de classes est de longueur .
@article{JTNB_2001__13_2_633_0, author = {Yamamura, Ken}, title = {Maximal unramified extensions of imaginary quadratic number fields of small conductors, {II}}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {633--649}, publisher = {Universit\'e Bordeaux I}, volume = {13}, number = {2}, year = {2001}, mrnumber = {1879676}, zbl = {1013.11076}, language = {en}, url = {http://archive.numdam.org/item/JTNB_2001__13_2_633_0/} }
TY - JOUR AU - Yamamura, Ken TI - Maximal unramified extensions of imaginary quadratic number fields of small conductors, II JO - Journal de théorie des nombres de Bordeaux PY - 2001 SP - 633 EP - 649 VL - 13 IS - 2 PB - Université Bordeaux I UR - http://archive.numdam.org/item/JTNB_2001__13_2_633_0/ LA - en ID - JTNB_2001__13_2_633_0 ER -
%0 Journal Article %A Yamamura, Ken %T Maximal unramified extensions of imaginary quadratic number fields of small conductors, II %J Journal de théorie des nombres de Bordeaux %D 2001 %P 633-649 %V 13 %N 2 %I Université Bordeaux I %U http://archive.numdam.org/item/JTNB_2001__13_2_633_0/ %G en %F JTNB_2001__13_2_633_0
Yamamura, Ken. Maximal unramified extensions of imaginary quadratic number fields of small conductors, II. Journal de théorie des nombres de Bordeaux, Volume 13 (2001) no. 2, pp. 633-649. http://archive.numdam.org/item/JTNB_2001__13_2_633_0/
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