Existence conjecture for projective crepant resolutions of quotient complete intersections

Let $G\subset\operatorname{SL}(r,\mathbb{C})$ be finite, and consider quotient complete-intersection singularities $\mathbb{C}^{r}/G$ in arbitrary dimension. Existence conjecture. All quotient complete-intersection singularities admit projective crepant resolutions. This conjecture concerns the existence problem for crepant desingularizations in dimensions $r\geq4$, where not every Gorenstein quotient singularity is expected to admit one.