ScalingStacks

Proposition 3.6. The weight complex functor yields an equivalence of categories

$$t:\operatorname{DTM}(k,\mathbb{Q})\to\operatorname{K}^{b}(\operatorname{DTM}(k,\mathbb{Q})^{w=0})\cong\operatorname{D}^{b}(\mathbb{Q}\operatorname{-mod}^{\mathbb{Z}})$$

where $\mathbb{Q}(1)[2]$ corresponds to the one-dimensional vector space in degree one $\mathbb{Q}\langle 1\rangle$ in the category $\mathbb{Q}\operatorname{-mod}^{\mathbb{Z}}$ of graded finite-dimensional vector spaces over $\mathbb{Q}.$