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Annulateurs circulaires et conjecture de Greenberg

Abstract : Given a real abelian field F with group G and an odd prime number ℓ, we define the circular subgroup of the pro-ℓ-group of logarithmic units and we show that for any Galois morphism ρ from the pro-ℓ-group of logarithmic units to Zℓ [G ], the image of the circular subgroup annihilates the ℓ-group of logarithmic classes. We deduce from this a proof of the logarithmic version of the Solomon conjecture. Using finally the deployment theorem of the tame ramification above the cyclotomic Zℓ-extension, we show that the same annihilation result holds for the image of the pro-ℓ-group of universal norms. This proves the Greenberg conjecture on the vanishing of the lamda invariant in the semi-simple case ℓ ∤ [F : Q], when the logarithmic class group of F is cyclic.
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https://hal.archives-ouvertes.fr/hal-02519397
Contributor : Jean-François Jaulent <>
Submitted on : Thursday, March 26, 2020 - 8:12:57 AM
Last modification on : Saturday, March 28, 2020 - 2:03:16 AM

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  • HAL Id : hal-02519397, version 1
  • ARXIV : 2003.12301

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INSMI | CNRS | IMB

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Jean-François Jaulent. Annulateurs circulaires et conjecture de Greenberg. 2020. ⟨hal-02519397⟩

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