Corps diédraux à multiplication complexe principaux

Yann Lefeuvre

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 1, page 67-103
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Lefeuvre, Yann. "Corps diédraux à multiplication complexe principaux." Annales de l'institut Fourier 50.1 (2000): 67-103. <http://eudml.org/doc/75420>.

@article{Lefeuvre2000,
abstract = {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.},
author = {Lefeuvre, Yann},
journal = {Annales de l'institut Fourier},
keywords = {CM-field; dihedral field; class number; relative class number; class field theory},
language = {fre},
number = {1},
pages = {67-103},
publisher = {Association des Annales de l'Institut Fourier},
title = {Corps diédraux à multiplication complexe principaux},
url = {http://eudml.org/doc/75420},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Lefeuvre, Yann
TI - Corps diédraux à multiplication complexe principaux
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 1
SP - 67
EP - 103
AB - 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.
LA - fre
KW - CM-field; dihedral field; class number; relative class number; class field theory
UR - http://eudml.org/doc/75420
ER -

References

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