Sur le radical kummérien des -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).
