3 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…

Modified André–Pink–Zannier conjecture. If $\mathcal{A}_{\Gamma}\cap\mathcal{V}$ is Zariski dense in $\mathcal{V}$, then one of the following holds:

Bounded-degree torsion sparsity conjecture. The set ${\mathbf{T}}(d)$ is not Zariski dense in $S$. The paper proves that this conjecture is equivalent to the strong uniform bounded…