Normalized volume and F-volume reduction conjecture

Let $x\in (X,\Delta)$ be a klt singularity over characteristic $0$, and let $(x_p\in (X_p,\Delta_p))$ be its reduction modulo $p\gg 0$. Reduction conjecture.

$$\widehat{\operatorname{vol}}(x,X,\Delta)=\lim_{p\to\infty}\operatorname{Fvol}(x_p,X_p,\Delta_p).$$

This conjecture proposes that normalized volume in characteristic zero is recovered as the limit of the $F$-volumes of reductions in positive characteristic.