Annulateurs de Stickelberger des groupes de classes logarithmiques

Jean-François Jaulent Acta Arithmetica MSC: Primary 11R23; Secondary 11R37, 11R70. DOI: 10.4064/aa201127-22-6 Published online: 18 October 2021

Abstract

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 component of the Bertrandias–Payan module. This leads to a very simple proof of annihilation results for the so-called wild étale $\ell $-kernels of $F$.

Authors

  • Jean-François JaulentInstitut de Mathématiques de Bordeaux
    Univ. Bordeaux & CNRS
    351 cours de la Libération
    F-33405 Talence Cedex, France
    e-mail

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