Extensions cycliques de degré ℓ de corps de nombres ℓ -réguliers

Florence Soriano

Journal de théorie des nombres de Bordeaux (1994)

  • Volume: 6, Issue: 2, page 407-420
  • ISSN: 1246-7405

Abstract

top
We determine all cyclic extensions L of prime degree ℓ over a ℓ -regular number field K containing the ℓ -roots of unity which are also l -regular. We classify these extensions according to the ramification index of the wild place ℒ in L / K and to the ℓ -valuation of the relative class number h L / K (which is the quotient h L / h K of the ordinary class numbers of L and K ). We study the case where the ℓ 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.

How to cite

top

Soriano, Florence. "Extensions cycliques de degré $\ell $ de corps de nombres $\ell $-réguliers." Journal de théorie des nombres de Bordeaux 6.2 (1994): 407-420. <http://eudml.org/doc/93611>.

@article{Soriano1994,
author = {Soriano, Florence},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = { of a number field; -regular number field; cyclic extensions},
language = {fre},
number = {2},
pages = {407-420},
publisher = {Université Bordeaux I},
title = {Extensions cycliques de degré $\ell $ de corps de nombres $\ell $-réguliers},
url = {http://eudml.org/doc/93611},
volume = {6},
year = {1994},
}

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
PB - Université Bordeaux I
VL - 6
IS - 2
SP - 407
EP - 420
LA - fre
KW - of a number field; -regular number field; cyclic extensions
UR - http://eudml.org/doc/93611
ER -

References

top
  1. [B] R. Berger, Class number parity and unit signature, Arch. Math.59 (1993), 427-435. Zbl0778.11062MR1185340
  2. [J] J.-F. Jaulent, L'arithmétique des l-extensions (Thèse), Publ. Math. Fac. Sci. Besançon, Théor. Nombres (1984/ 1985, 1985/1986 (1986)), 13-43, 163-178. Zbl0601.12002
  3. [JN] J.-F. Jaulent & T. NguyenQUANG DO, Corps p-rationnels, corps p-réguliers, et ramification restreinte, J. Théor. Nombres Bordeaux5 (1994), 343-363. Zbl0957.11046MR1265910
  4. [GJ] G. Gras et J.-F. Jaulent, Sur les corps de nombres réguliers, Math.Z.202 (1989), 343-365. Zbl0704.11040MR1017575
  5. [S] J.-P. Serre, Corps Locaux, Hermann, Paris (1968), 17-34, 211-238. Zbl0137.02601MR354618

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.