Note sur la conjecture de Leopoldt

TL;DR

This paper proves that number fields with arbitrary degree and weak ramification satisfy the Leopoldt conjecture regarding the l-adic rank of their units, advancing understanding in algebraic number theory.

Contribution

It establishes the Leopoldt conjecture for a new class of number fields characterized by weak ramification.

Findings

Leopoldt conjecture holds for weakly ramified number fields.

Extension of validity of Leopoldt conjecture to arbitrary degree fields.

Provides new insights into the structure of units in number fields.

Abstract

We prove that number fields with arbitrary degree but weak ramification satisfy the Leopoldt conjecture on the l-adic rank of the group of units