3 problems

Mordell–Pink–Zywina conjecture. There exists a density one set of places such that the reduction $X_v$ is isogenous to the $d$-th power of a simple abelian variety. This predicts i…

Let $K$ be a number field and let $A/K$ be a principally-polarizable abelian surface whose absolute endomorphism ring satisfies … Let $\pi_{\operatorname{split}}(A/K,z)$ count prim…

The split-reduction growth conjecture. For sufficiently general $A$, the counting function $\pi_{\operatorname{split}}(A/K,z)$ grows like $\sqrt z/\log z$.