Reid's derived McKay correspondence conjecture

Let $G$ be a finite group acting linearly on $\mathbb C^n$, and suppose that a crepant resolution of the quotient exists,

$$\widetilde X\longrightarrow \mathbb C^n/G.$$

Reid's derived McKay correspondence conjecture. There is an equivalence

$$D^b(\operatorname{Coh}\widetilde X)\simeq D^b_G(\mathbb C^n),$$

where $D^b_G(\mathbb C^n)$ is the bounded derived category of $G$-equivariant coherent sheaves. The conjecture extends the Bridgeland–King–Reid correspondence beyond the cases covered by its fiber-product hypothesis; the source notes that this hypothesis is automatic in dimension at most three but can fail in dimension four.