ScalingStacks

Proof. Using the conditions on $p$ [Ebe21, Theorem 1.1] shows that the motive $\operatorname{M}(\mu^{-1}(\{x\}))$ of a Springer fiber is pure Tate which implies (PT). Moreover, there are only finitely many $G$-orbits in $\mathcal{N}_{nil},$ see [Car93], which shows that condition (FO) holds. ∎