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user19475
user19475

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?

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?

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?

Source Link
user19475
user19475

Relation between motivic homotopy category and the derived category of motives

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?