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Given a real abelian field F with group G and an odd prime number {\ell}, we define the circular subgroup of the pro-{\ell}-group of logarithmic units and we show that for any Galois morphism $\rho$ from the pro-{\ell}-group of logarithmic units to Z{\ell} [G ], the image of the circular subgroup annihilates the {\ell}-group of logarithmic classes. We deduce from this a proof of a logarithmic version of Solomon conjecture., Comment: in French

For any odd prime number $\ell$ and any abelian number field F containing the $\ell$-th roots of unity, we show that the Stickelberger ideal annihilates the imaginary component of the $\ell$-group of logarithmic classes and that its reflection annihilates the real componen of the Bertrandias-Payan module. As a consequence we obtain a very simple proof of annihilation results for the so-called wild {\'e}tale $\ell$-kernels of F ., Comment: in French

RésuméNous étudions la ℓ-partie des noyaux étales sauvage WK2i(F) d'un corps de nombres arbitraire F en liaison avec l'arithmétique des classes logarithmiques. Nous en déduisons notamment des formules de rang, des résultats de périodicité et de réflexion, des caractérisations de la trivialité, ainsi que diverses conséquences.AbstractWe study the ℓ-part of the wild étale kernels WK2i(F) of an arbitary number field F for a given prime ℓ in connection with the logarithmic ℓ-class groups Cℓ˜F. From the logarithmic arithmetic we deduce rank formulas, periodicity and reflection theorems, triviality characterizations and various consequences.