Topological behaviour of logarithmic invariants
Language
en
Document de travail - Pré-publication
English Abstract
Let $\ell$ be a rational prime number and $K$ a number field. We prove that the logarithmic module $X_{d}$ attached to a $\mathbb{Z}_{\ell}^{d}$-extension $K_{d}$ of $K$ is a noetherian $\Lambda_{d}$-module. Moreover, under ...Read more >
Let $\ell$ be a rational prime number and $K$ a number field. We prove that the logarithmic module $X_{d}$ attached to a $\mathbb{Z}_{\ell}^{d}$-extension $K_{d}$ of $K$ is a noetherian $\Lambda_{d}$-module. Moreover, under the Gross-Kuz'min conjecture we prove that it is also torsion. We exploit this fact to deduce local and global information of the logarithmic invariants $\tilde{\mu}$ and $\tilde{\lambda}$ of $\mathbb{Z}_{\ell}$-extensions.Read less <
English Keywords
Iwasawa invariants
logarithmic class groups
logarithmic invariants
Origin
Hal imported