Perverse equivalence conjecture for cyclic-defect unipotent blocks

Let $B$ be a unipotent block of $kG$ with cyclic defect groups, and let $B'$ be its Brauer correspondent. Let $\pi_{\kappa/d}$ be the perversity function defined from the generic degrees, and use the specified bijection between the simple $B$-modules and simple $B'$-modules. Cyclic-defect perverse equivalence conjecture. The perversity function $\pi_{\kappa/d}$ and this bijection induce a perverse equivalence between $B$ and $B'$. This is the cyclic-defect case of the proposed geometric form of Broué's conjecture; the source gives no resolution of the assertion as stated.