5 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

Let $H\leq J$ be subgroups of a free group $\mathbf{F}$. Let $\mathbf{F}'$ be a free extension of $\mathbf{F}$, meaning that $\mathbf{F}\leq\mathbf{F}'$ and $\mathbf{F}'$ is free,…

Let $\mathbf{F}$ be a free group, and let $H\leq J\leq\mathbf{F}$. For a basis $X$ of $\mathbf{F}$, write $H\leq_{{\scriptscriptstyle \overset{\twoheadrightarrow}{X}}}J$ when the c…