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 and J.-F Jaulent’s results.
@article{JTNB_1994__6_2_407_0, author = {Soriano, Florence}, title = {Extensions cycliques de degr\'e $\ell $ de corps de nombres $\ell $-r\'eguliers}, journal = {Journal de Th\'eorie des Nombres de Bordeaux}, pages = {407--420}, publisher = {Universit\'e Bordeaux I}, volume = {6}, number = {2}, year = {1994}, zbl = {0834.11049}, mrnumber = {1360653}, language = {fr}, url = {http://www.numdam.org/item/JTNB_1994__6_2_407_0/} }
TY - JOUR AU - Soriano, Florence TI - Extensions cycliques de degré $\ell $ de corps de nombres $\ell $-réguliers JO - Journal de Théorie des Nombres de Bordeaux PY - 1994 DA - 1994/// SP - 407 EP - 420 VL - 6 IS - 2 PB - Université Bordeaux I UR - http://www.numdam.org/item/JTNB_1994__6_2_407_0/ UR - https://zbmath.org/?q=an%3A0834.11049 UR - https://www.ams.org/mathscinet-getitem?mr=1360653 LA - fr ID - JTNB_1994__6_2_407_0 ER -
Soriano, Florence. Extensions cycliques de degré $\ell $ de corps de nombres $\ell $-réguliers. Journal de Théorie des Nombres de Bordeaux, Tome 6 (1994) no. 2, pp. 407-420. http://www.numdam.org/item/JTNB_1994__6_2_407_0/
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