The strong saturation conjecture for smooth quasi-projective varieties

Let $V$ be a smooth strongly ${\cal L}$-saturated quasi-projective variety over the relevant number field, with the adelic polarization understood as in the source. The complex analytic variety associated with $V$ is $V({\bf C})$.

Strong saturation conjecture. The complex analytic variety $V({\bf C})$ is ${\cal L}$-primitive.

This is the stronger geometric reduction step in the paper's arithmetic counting strategy. It overlaps with the first main Diophantine conjecture, but its supplied formulation is specialized to smooth varieties; the source gives no resolution status.