The virtually nilpotent fundamental-group conjecture for h-special and special varieties

Let $X$ be an $h$-special or special smooth quasi-projective variety, where $h$-special means that the relation on pairs of points generated by chains of entire curves is Zariski dense in $X\times X$.

Nilpotency conjecture. The fundamental group $\pi_1(X)$ is virtually nilpotent.

This is presented as the revision of Campana's virtually abelian conjecture for non-compact smooth quasi-projective varieties. It is a restatement of the revised conjecture already given earlier in the paper, so it is merged with that row.