The crepant resolution conjecture for quotient singularities

Let $V$) be a complex vector space and let $\Gamma\subset\operatorname{SU}(m/2)$ be finite. Let $(M,\rho)$ be a crepant resolution of $V/\Gamma$, and let the age of a conjugacy class of $\Gamma$ be the grading appearing in the conjecture. The crepant resolution conjecture. There exists a basis of $H^\bullet(M,\mathbb{Q})$ consisting of algebraic cycles in correspondence with the conjugacy classes of $\Gamma$, with a conjugacy class of age $k$ corresponding to a cycle in $H^{2k}(M,\mathbb{Q})$. In particular, $H^\bullet(M;\mathbb{Q})$ is concentrated in even degrees and $\chi(M)$ equals the number of conjugacy classes of $\Gamma$. This is the string-theoretic prediction relating the topology of a crepant resolution to the representation theory of the quotient group; its general status is not resolved by the source.