Sur le radical kummérien des $\mathbb {Z}_\ell $-extensions
Acta Arithmetica, Tome 175 (2016) no. 3, pp. 245-253
Cet article a éte moissonné depuis 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
@article{10_4064_aa8366_7_2016,
author = {Jean-Fran\c{c}ois Jaulent},
title = {Sur le radical kumm\'erien des $\mathbb {Z}_\ell $-extensions},
journal = {Acta Arithmetica},
pages = {245--253},
year = {2016},
volume = {175},
number = {3},
doi = {10.4064/aa8366-7-2016},
language = {fr},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa8366-7-2016/}
}
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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