9 problems

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

Universal-extension compatibility conjecture. The map $\Psi$ is a map of $D$-group schemes for abelian schemes $A$.

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…

Let $\mathcal{A}\rightarrow S$ be an abelian scheme over a number field $K$. For $d\in\mathbb{N}$, let $\mathcal{A}^{[>d]}$ be the union of all group subvarieties of the fibers of…

Let $\mathcal{A}\rightarrow C$ be an abelian scheme on a curve over a number field $K$ whose generic fiber is geometrically simple of dimension at least $2$. Let…

Let $\phi\colon \mathcal A\to S$ be an abelian scheme of relative dimension $g$ without fixed part. Write $M^{\textrm{rel}}_\sigma$ for the relative monodromy group of a section…

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…

Finiteness conjecture. The group $\Sha({\mathscr{A}}/X)$ is finite.

Let $C$ be the base curve, let ${\mathcal A}$ be the abelian scheme appearing in the source, and let … The two groups are compared after tensoring with $\mathbb C$ via the de Rham–…