7 problems

Let $\mathcal{A}\rightarrow S$ be the abelian scheme in the paper, and let $\mathcal{X}\subseteq\mathcal{A}$ be a subvariety. For $t\in\mathbb{N}$, let $\mathcal{A}_{(\leq t)}$ be…

Bounded-height conjecture. At least one of the following holds: $(f,a)$ or $(g,b)$ is isotrivial; there exist $m,n\geq 0$ such that $f^m(a)=g^n(b)$; or $S$ has bounded height.

Bounded height conjecture. The height $h_L$ is bounded from above on

Let $G$ be a group variety and let $V\subset G$ be irreducible. A maximal $V$-torsion anomalous point is a point that is a maximal $V$-torsion anomalous variety under the terminolo…

Let $G$ be a group variety and let $V\subset G$ be irreducible. A maximal $V$-torsion anomalous point is a point that is a maximal $V$-torsion anomalous variety under the terminolo…

Let $G$ be a group variety, and let $V\subset G$ be irreducible. Let $V^{oa}$ be the set of points of $V$ outside the $V$-anomalous varieties, and define … where the union is over…

Let $A$ be a semi-abelian variety, let $V$ be an irreducible algebraic subvariety of dimension $d$ defined over $\overline{\mathbb{Q}}$, and let $\Gamma$ be a finite-rank subgroup…