Normes cyclotomiques naïves et unités logarithmiques

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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https://hal.archives-ouvertes.fr/hal-01361276
Contributor : Jean-François Jaulent <>
Submitted on : Tuesday, February 14, 2017 - 7:44:08 AM
Last modification on : Thursday, January 11, 2018 - 6:21:23 AM
Long-term archiving on : Monday, May 15, 2017 - 12:31:13 PM

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  • HAL Id : hal-01361276, version 2
  • ARXIV : 1609.01901

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Jean-François Jaulent. Normes cyclotomiques naïves et unités logarithmiques. 2017. ⟨hal-01361276v2⟩

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