Sur la capitulation pour le module de Bertrandias-Payan

TL;DR

This paper computes the capitulation kernel for the Bertrandias-Payan module in arbitrary ll-extensions of number fields satisfying Leopoldt's conjecture, linking it to locally cyclotomic towers.

Contribution

It provides a general computation of the capitulation kernel for the Bertrandias-Payan module in ll-extensions, extending previous results to more general cases.

Findings

Capitulation kernel computed for Bertrandias-Payan module in ll-extensions.

Relation established between triviality of the module and locally cyclotomic towers.

Results hold under Leopoldt's conjecture.

Abstract

We compute the capitulation kernel for the module of Bertrandias-Payan in an arbitrary $\ell$-extension of number fields which satisfies the Leopoldt conjecture. As a consequence we relate the existence of extensions with trivial such module to the classical problem of locally cyclotomic towers.