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arXiv · 1609.01901

Normes cyclotomiques na{ï}ves et unit{é}s logarithmiques

Jean-François Jaulent
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Abstract

We compute the Z-rank of the subgroup of elements of the multiplicative group of a number field K that are norms from every finite level of the cyclotomic Z{\ell}-extension of K. Thus we compare its {\ell}-adification with the group of logarithmic units of K. By the way we point out an easy proof of the Gross-Kuz'min conjecture for {\ell}-undecomposed extensions of abelian fields.

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Jean-François Jaulent. 2017-02-16. Normes cyclotomiques na{ï}ves et unit{é}s logarithmiques. https://arxiv.org/abs/1609.01901

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