Minoration de la hauteur de Weil dans un compositum de corps de rayon

TL;DR

This paper proves that under certain conditions, the compositum of a family of fields satisfies Property (B), which relates to lower bounds on the Weil height of points of infinite order, contributing to Lehmer's conjecture.

Contribution

It establishes that the compositum of multiple fields satisfies Property (B) under specific uniformity conditions, advancing understanding of height bounds in algebraic number theory.

Findings

Proves Property (B) for compositum of fields under uniformity conditions

Provides new lower bounds for Weil heights in compositum fields

Contributes to the study of Lehmer's conjecture and height bounds

Abstract

The study of Property (B) starts as a special case of Lehmer's conjecture. An algebraic field is said to satisfy Property (B) if there exists a positive constant bounding by below the height of every point of infinite order. In this paper we prove that, under certain uniformity conditions, the compositum of a familly of fields satisfies Property (B).