4 problems

Geometric Bogomolov conjecture. If $X$ has dense small points, then $X$ should be special.

Geometric Bogomolov conjecture in the remaining case. Then $X$ is a torsion subvariety.

Let $C$ be a smooth projective curve over $\overline{K}$ of genus at least $2$, let $J_C$ be its Jacobian, let $D$ be a degree-one divisor, let $j_D:C\to J_C$ be the associated emb…

Let $A$ be a nowhere degenerate abelian variety over $\overline{K}$, meaning that its abelian variety structure has no nontrivial degenerate part, and let $X$ be a closed subvariet…