Sur le radical kummérien des $\mathbb {Z}_\ell $-extensions
Acta Arithmetica, Tome 175 (2016) no. 3, pp. 245-253
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
On the basis of a previous work, we elaborate a new description of the Kummer radical associated to the first layers of $\mathbb{F}_2$-extensions of a number field $K$, by using inverse limits for the norm maps in the cyclotomic $\mathbb{F}_2$-extension $K_\infty/K$. Our main result contains, as an obvious consequence, the inclusions provided by Soogil Seo in a series of papers. In the same way we also give in the last section a similar description of the Tate kernel for universal symbols in $K_2(K)$.
Mots-clés :
basis previous work elaborate description kummer radical associated first layers mathbb extensions number field nbsp using inverse limits norm maps cyclotomic mathbb extension infty main result contains obvious consequence inclusions provided soogil seo series papers section similar description tate kernel universal symbols
Affiliations des auteurs :
Jean-François Jaulent 1
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author = {Jean-Fran\c{c}ois Jaulent},
title = {Sur le radical kumm\'erien des $\mathbb {Z}_\ell $-extensions},
journal = {Acta Arithmetica},
pages = {245--253},
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volume = {175},
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TY - JOUR
AU - Jean-François Jaulent
TI - Sur le radical kummérien des $\mathbb {Z}_\ell $-extensions
JO - Acta Arithmetica
PY - 2016
SP - 245
EP - 253
VL - 175
IS - 3
PB - mathdoc
UR - http://geodesic.mathdoc.fr/articles/10.4064/aa8366-7-2016/
DO - 10.4064/aa8366-7-2016
LA - fr
ID - 10_4064_aa8366_7_2016
ER -
Jean-François Jaulent. Sur le radical kummérien des $\mathbb {Z}_\ell $-extensions. Acta Arithmetica, Tome 175 (2016) no. 3, pp. 245-253. doi: 10.4064/aa8366-7-2016
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