G{\'e}n{\'e}ralisation d'un th{\'e}or{\`e}me de Greenberg

TL;DR

This paper proposes a broad conjecture linking characteristic polynomials of certain Iwasawa modules to classical conjectures in number theory, extending previous results on module semi-simplicity and isomorphisms.

Contribution

It formulates a general conjecture unifying Greenberg's semi-simplicity and Kuz'min's isomorphism with classical conjectures of Leopoldt and Gross-Kuz'min.

Findings

Conjecture is equivalent to Leopoldt and Gross-Kuz'min conjectures

Extends Greenberg's semi-simplicity result

Provides an isomorphism of Kuz'min

Abstract

We formulate a general conjecture on the characteristic polynomials of S-decomposed T-ramified Iwasawa modules over the cyclotomic Z {\ell}-extension of a number field. We show that this conjecture is equivalent to the conjunctions of the classical conjectures of Leopoldt and of Gross-Kuz'min. We so extend a result of semi-simplicity of Greenberg and, by the way, an isomorphism of Kuz'min.