Ramifications minimales

Georges Gras

Journal de théorie des nombres de Bordeaux (2000)

  • Volume: 12, Issue: 2, page 423-435
  • ISSN: 1246-7405

Abstract

top
We apply, for the notion of extension (cyclic of degree p ) with minimal ramification, the technics of “reflection” which allow a very simple characterization of these extensions by mean of a governing field.

How to cite

top

Gras, Georges. "Ramifications minimales." Journal de théorie des nombres de Bordeaux 12.2 (2000): 423-435. <http://eudml.org/doc/248495>.

@article{Gras2000,
abstract = {Nous appliquons à la notion d’extension (cyclique de degré $p$) à ramification minimale, les techniques de “ réflexion ” qui permettent une caractérisation très simple de ces extensions à l’aide d’un corps gouvernant.},
author = {Gras, Georges},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {governing field; minimal ramification; reflection theorem},
language = {fre},
number = {2},
pages = {423-435},
publisher = {Université Bordeaux I},
title = {Ramifications minimales},
url = {http://eudml.org/doc/248495},
volume = {12},
year = {2000},
}

TY - JOUR
AU - Gras, Georges
TI - Ramifications minimales
JO - Journal de théorie des nombres de Bordeaux
PY - 2000
PB - Université Bordeaux I
VL - 12
IS - 2
SP - 423
EP - 435
AB - Nous appliquons à la notion d’extension (cyclique de degré $p$) à ramification minimale, les techniques de “ réflexion ” qui permettent une caractérisation très simple de ces extensions à l’aide d’un corps gouvernant.
LA - fre
KW - governing field; minimal ramification; reflection theorem
UR - http://eudml.org/doc/248495
ER -

References

top
  1. [CDO] H. Cohen, F. Diaz Y Diaz, M. Olivier, Computing ray class groups, conductors and discriminants. Math. of Comp.67 (1998), 773-795. Zbl0929.11064MR1443117
  2. [Col] H. Cohen, Advanced topics in computational number theory. G.T.M. 193, Springer-Verlag (2000). Zbl0977.11056MR1728313
  3. [Co2] H. Cohen, A survey of computational class field theory. J. Théorie des Nombres de Bordeaux11 (1999), 1-13. Zbl0949.11063MR1730429
  4. [Cor] G. Cornell, The sructure of the ray class group. In: Algebraic Number Theory, RIMS, Kokyuroku (1987). Zbl0636.12007
  5. [Fi] C. Fieker, Computing class fields via the Artin map. Jour. Symb. Comput. (to appear). Zbl0982.11074MR1826583
  6. [G1] G. Gras, Pratique de la théorie du corps de classes global. En préparation. 
  7. [G2] G. Gras, Théorèmes de réflexion. J. Théorie des Nombres de Bordeaux10 (1998), 399-499. Zbl0949.11058MR1828251
  8. [GM] G. Gras, A. Munnier, Extensions cycliques T-totalement ramifiées. Publ. Math. Fac. Sci. Besançon (Théorie des Nombres), Années 1996/97-1997/98. 
  9. [J] J.-F. Jaulent, Théorie -adique globale du corps de classes. J. Théorie des Nombres de Bordeaux10 (1998), 355-397. Zbl0938.11052MR1828250
  10. [M1] J. Martinet, Méthodes géométriques dans la recherche des petits discriminants. Séminaire de Théorie des Nombres de Paris 1983-1984, Birkhäuser, Bâle (1985), 147-179. Zbl0567.12009MR902831
  11. [M2] J. Martinet, On some 2-class fields. Communication privée. 
  12. [N] J. Neukirch, Über das Einbettungsproblem der algebraischen Zahlentheorie. Invent. Math.21 (1973), 59-116. Zbl0267.12005MR337894
  13. [S] I.R. Šafarevi, Extensions with given points of ramification. Publ. Math. Inst. Hautes Etudes Sci.18 (1964), 71-95; A.M.S. Transl. (2) 59 (1966), 128-149. MR176979
  14. [St] P. Stevenhagen, Ray class groups and governing fields. Ph. D. Thesis, University of Amsterdam, Amsterdam (1988). Zbl0701.11056MR1052942

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.