ScalingStacks

Theorem (Theorem 5.2). Under a standard assumption on $p,$ there is an equivalence of categories

$$\operatorname{DM}^{Spr}_{G\times\mathbb{G}_{m}}(\mathcal{N}_{nil},\mathbb{Q})\cong\operatorname{D}^{\mathbb{Z}}_{\operatorname{perf}}(\overline{\mathbb{H}}(G))$$

between the category of Springer motives on the nilpotent cone $\mathcal{N}_{nil}$ and the perfect derived category of graded modules of $\overline{\mathbb{H}}(G).$