Extensions cycliques de degré de corps de nombres -réguliers
We determine all cyclic extensions of prime degree over a -regular number field containing the -roots of unity which are also -regular. We classify these extensions according to the ramification index of the wild place in and to the -valuation of the relative class number (which is the quotient of the ordinary class numbers of and ). We study the case where the is odd prime, since the even case was studien by R. Berger. Our genus theory methods rely essentially on G. Gras...