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What's the relation between the pointed motivic homotopy category $\mathcal{H}_*(k)$ and the derived category of motives $\mathbf{DM}^-_{eff}(k)$ besides the representability of motivic cohomology in the homotopy category? I think there is a functor $\mathcal{H}(k) \to \mathbf{DM}^-_{eff}(k)$. How far is it from being full and faithful? |
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Relation between motivic homotopy category and the derived category of motivesWhat's the relation between the pointed motivic homotopy category $\mathcal{H}_*(k)$ and the derived category of motives $\mathbf{DM}^-_{eff}(k)$ besides the representability of motivic cohomology in the homotopy category?
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