Craven–Rouquier perversity conjecture for Broué's equivalence

Let $C$ be the cohomology complex associated with the relevant Deligne–Lusztig variety, and let $\mathcal{S}_{B_0(H)}$ denote the simple-module indexing set for the local principal block, with $H=N_G(D)$. Let $\pi_{\kappa/d}:\mathcal{S}_{B_0(H)}\to\mathbb{Z}_{\geqslant 0}$ be obtained from the unitriangular decomposition matrix and the unique-degree map on unipotent characters. Craven–Rouquier conjecture. The derived equivalence induced by $C$ is a perverse equivalence, with $\pi_{\kappa/d}$ as its perversity function. The source explicitly says that these conjectures remain open and have been proved only in restricted cases.