Corps diédraux à multiplication complexe principaux
Annales de l'Institut Fourier, Volume 50 (2000) no. 1, p. 67-103

We determine all the dihedral CM fields with relative class number one, then all of them with class number one: there are 32 such non-abelian fields with class number one. This is the first example of resolution of the class number one problem for non-abelian normal CM-fields of a given Galois group.

Nous déterminons tous les corps diédraux à multiplication complexe de nombres de classes relatif un, puis ceux de nombre de classes un : il y a 32 tels corps non-abéliens principaux. C’est le premier exemple, dans ce cadre assez général, de résolution du problème de nombre de classes un pour les corps galoisiens à multiplication complexe avec un type de groupe de Galois non-abélien fixé.

@article{AIF_2000__50_1_67_0,
     author = {Lefeuvre, Yann},
     title = {Corps di\'edraux \`a multiplication complexe principaux},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {50},
     number = {1},
     year = {2000},
     pages = {67-103},
     doi = {10.5802/aif.1747},
     zbl = {0952.11024},
     mrnumber = {2001g:11166},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2000__50_1_67_0}
}
Lefeuvre, Yann. Corps diédraux à multiplication complexe principaux. Annales de l'Institut Fourier, Volume 50 (2000) no. 1, pp. 67-103. doi : 10.5802/aif.1747. http://www.numdam.org/item/AIF_2000__50_1_67_0/

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