ScalingStacks

Proof. Lemma 3.1 implies that $\operatorname{DTM}(k,\mathbb{Q})^{w=0}$ is tilting in $\operatorname{DTM}(k,\mathbb{Q}).$ Further, $\operatorname{DM}$ admits an enhancement as stable $\infty$-category. The statement follows from Corollary 2.16. ∎