4 problems

David-Hindry's conjecture. For every integer $n\in\mathbb{N}$, there is a constant $c(A/K,\mathcal{L},n)>0$ such that, for every $n$-tuple $(P_1,\ldots,P_n)$ of points of infinite…

Let $K$ be a number field, and let $G$ be either $\mathbb{G}_m^t$ for some $t\in\mathbb{Z}_{\geq 0}$ or an abelian variety over $K$. Let $\Gamma\subset G(\overline{K})$ be a subgro…

Abelian Lehmer problem. There is a constant $c(A/K,\mathcal{L})>0$ such that, for every point $P\in A(\overline{K})$ of infinite order modulo every proper abelian subvariety of $A$…

Let $K$ be a number field, let $G$ be a semiabelian variety over $K$, and let $\Gamma\subset G(\overline{K})$ be a subgroup of finite rank. For a subvariety $V\subset G$, write…