3 problems

Realization equivalence conjecture. The functor $\m{Re}$ induces an equivalence of $\QQ$-linear triangulated symmetric monoidal categories

Let $k$ be a field, let $\mathcal{SH}(k)$ be its motivic stable homotopy category, and let $\mathrm{Re}\colon \mathcal{SH}(k)\to \mathcal{C}$ be an abstract realization functor. Le…

Let ${\rm DM}_{gm}(\mathbb{C})_{\mathbb{Q}}$ be the category of rationalized geometric motives over the complex numbers, and let … be Betti realization. Equivalently, let … be the…