Rank of a free pro-p-extension of a number field.

Arthur Lannuzel

Publicacions Matemàtiques (2002)

  • Volume: 46, Issue: 1, page 201-219
  • ISSN: 0214-1493

Abstract

top
For an algebraic number field k and a prime number p (if p = 2, we assume that μ4 ⊂ k), we study the maximal rank ρk of a free pro-p- extension of k. We give various interpretations of 1 + r2(k) - ρk. The first uses Iwasawa theory, the second uses the envelope of a module and the third is local-global. These expressions confirm that 1 + r2 - ρk is related to the torsion of a certain Iwasawa module, hence to the dualizing module of a certain Galois group (under Leopoldt's conjecture).

How to cite

top

Lannuzel, Arthur. "Sur le rang d'une extension pro-p-libre d'un corps de nombres.." Publicacions Matemàtiques 46.1 (2002): 201-219. <http://eudml.org/doc/41449>.

@article{Lannuzel2002,
author = {Lannuzel, Arthur},
journal = {Publicacions Matemàtiques},
keywords = {Teoría algebraica de números; Teoría de Galois; Teoría de Iwasawa; pro--free extensions},
language = {fre},
number = {1},
pages = {201-219},
title = {Sur le rang d'une extension pro-p-libre d'un corps de nombres.},
url = {http://eudml.org/doc/41449},
volume = {46},
year = {2002},
}

TY - JOUR
AU - Lannuzel, Arthur
TI - Sur le rang d'une extension pro-p-libre d'un corps de nombres.
JO - Publicacions Matemàtiques
PY - 2002
VL - 46
IS - 1
SP - 201
EP - 219
LA - fre
KW - Teoría algebraica de números; Teoría de Galois; Teoría de Iwasawa; pro--free extensions
UR - http://eudml.org/doc/41449
ER -

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.