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

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     title = {Corps di\'edraux \`a multiplication complexe principaux},
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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://archive.numdam.org/articles/10.5802/aif.1747/

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