3 problems

Rank-greater-than-two conjecture. The original Miasnikov–Ventura–Weil conjecture holds for $H\leq K\leq F_Y$ whenever $|Y|>2$.

Parzanchevski–Puder conjecture. If, for every free extension $F'$ of $F_Y$ and every basis $X$ of $F'$, the morphism

Miasnikov–Ventura–Weil conjecture. If the morphism