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1 results

A new way to tackle a conjecture of Rémond
Part of
- Arithmetic algebraic geometry
- Algebraic number theory: global fields
Arnaud Plessis
Journal:

Canadian Journal of Mathematics / Volume 76 / Issue 6 / December 2024

Published online by Cambridge University Press:

31 October 2023, pp. 2049-2072

Print publication:

December 2024
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Let $\Gamma \subset \overline {\mathbb {Q}}^*$ 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 $\mathbb {Q}(\Gamma _{\mathrm {div}})^*\backslash \Gamma _{\mathrm {div}}$ is bounded from below by a positive constant depending only on $\Gamma $. In this paper, we propose a new way to tackle this problem.