A new way to tackle a conjecture of R\'emond

Arnaud Plessis

A new way to tackle a conjecture of R\'emond

Number Theory 2023-02-13 v3

Authors: Arnaud Plessis

Abstract

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

Keywords

remond conjecture zilber-pink conjecture logarithmic weil height division group finitely generated subgroup

Cite

@article{arxiv.2201.06226,
  title  = {A new way to tackle a conjecture of R\'emond},
  author = {Arnaud Plessis},
  journal= {arXiv preprint arXiv:2201.06226},
  year   = {2023}
}

Comments

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

A new way to tackle a conjecture of R\'emond

Abstract

Keywords

Cite

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