Normes cyclotomiques naïves et unités logarithmiques

2016/09/07 by Jaulent, Jean-François
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1609.01901

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 Zℓ-extension of K. Thus we compare its ℓ-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 ℓ-undecomposed extensions of abelian fields.

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