A new way to tackle a conjecture of Rémond

Abstract

Let $\Gamma \subset {\bar{\mathbb{Q}}}^{\ast }$ be a finitely generated subgroup. Denote by ${\Gamma }_{\mathrm{div}}$ its division group. A recent conjecture due to Rémond, related to the Zilber-Pink conjecture, predicts that the absolute logarithmic Weil height of an element of $\mathbb{Q}({\Gamma }_{\mathrm{div}}{)}^{\ast }\backslash {\Gamma }_{\mathrm{div}}$ is bounded from below by a positive constant depending only on $\Gamma$. In this paper, we propose a new way to tackle this problem.

arXiv commentTheorem 1.2 has been added and the organization of this paper is largely different, although the proofs of theorems remain the same

Cited by in corpus (1)

• On the Northcott property for special values of L-functions