Note sur la conjecture de Greenberg

Abstract : We use logarithmic ℓ-class groups to take a new view on Greenberg's conjecture about Iwasawa ℓ-invariants of a totally real number field K. By the way we recall and complete some classical results. Under Leopoldt's conjecture, we prove that Greenberg's conjecture holds if and only if the logarithmic classes of K principalize in the cyclotomic Zℓ-extensions of K. As an illustration of our approach, in the special case where the prime ℓ splits completely in K, we prove that the sufficient condition introduced by Gras just asserts the triviality of the logarithmic class group of K. Last, in the abelian case, we provide an explicit description of the circular class groups in connexion with the so-called weak conjecture.
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Contributor : Jean-François Jaulent <>
Submitted on : Sunday, April 29, 2018 - 9:00:47 AM
Last modification on : Thursday, May 3, 2018 - 1:14:26 AM


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  • HAL Id : hal-01407300, version 3
  • ARXIV : 1612.00718



Jean-François Jaulent. Note sur la conjecture de Greenberg. Journal of the Ramanujan Mathematical Society, Ramanujan Mathematical Society, A paraître. 〈hal-01407300v3〉



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