Broué–Malle–Rouquier freeness conjecture for generic Hecke algebras

Let $W\subset GL(V)$ be a complex reflection group, let $R(W)$ be its associated Laurent polynomial ring, and let $\mathcal{H}(W)$ be the associated generic Hecke algebra over $R(W)$. Broué–Malle–Rouquier freeness conjecture. The algebra $\mathcal{H}(W)$ is a free $R(W)$-module of rank $|W|$. This conjecture is now a theorem; it generalises the corresponding freeness result for real reflection groups and is fundamental to the structure theory of Hecke algebras of complex reflection groups.