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}, pages = {67--103}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {50}, number = {1}, year = {2000}, doi = {10.5802/aif.1747}, zbl = {0952.11024}, mrnumber = {2001g:11166}, language = {fr}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1747/} }
TY - JOUR AU - Lefeuvre, Yann TI - Corps diédraux à multiplication complexe principaux JO - Annales de l'Institut Fourier PY - 2000 SP - 67 EP - 103 VL - 50 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.1747/ DO - 10.5802/aif.1747 LA - fr ID - AIF_2000__50_1_67_0 ER -
%0 Journal Article %A Lefeuvre, Yann %T Corps diédraux à multiplication complexe principaux %J Annales de l'Institut Fourier %D 2000 %P 67-103 %V 50 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.1747/ %R 10.5802/aif.1747 %G fr %F 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. https://aif.centre-mersenne.org/articles/10.5802/aif.1747/
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