Sur le radical kummérien des $\mathbb {Z}_\ell $-extensions
Volume 175 / 2016
Acta Arithmetica 175 (2016), 245-253
MSC: Primary 11R23; Secondary 11R37.
DOI: 10.4064/aa8366-7-2016
Published online: 23 September 2016
Abstract
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 $K_2(K)$.
