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Sur le radical kummérien des $\mathbb {Z}_\ell $-extensions

Volume 175 / 2016

Jean-François Jaulent 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 $K_2(K)$.

Authors

  • Jean-François JaulentUniversité de Bordeaux & CNRS
    Institut de Mathématiques de Bordeaux
    351, cours de la Libération
    33405 Talence Cedex, France
    e-mail

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