2 problems

Full-faithfulness conjecture. The functor $\Theta$ is fully faithful. This would embed the homotopy theory of $DG$-schemes into the homotopy theory of geometric stacks over the mod…

Let $S$ be a derived scheme. Write $\mathrm{H}\mathbb Q$ for the rational motivic cohomology spectrum over $S$, and let $\mathbbm{1}_{\mathbb Q}^+$ denote the positive eigenspace i…