Annulateurs de Stickelberger des groupes de classes logarithmiques
Volume 201 / 2021
Acta Arithmetica 201 (2021), 241-253
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 $F$.
