11
votes
3answers
541 views

Applications of homotopy purity theorem of Morel-Voevodsky

One of the most important theorems in motivic homotopy theory is the homotopy purity theorem of Morel-Voevodsky which says that the motivic Thom space of the normal bundle $\mathcal N_{Z/X}$ of a ...
3
votes
0answers
291 views

Two questions on motivic homotopy theory

I am a beginner in motivic homotopy theory and motivic cohomology and have just begun reading books by Dundas et al. and Mazza-Voevodsky-Weibel. I have two basic questions: Why is the question of ...
0
votes
0answers
100 views

Reference for Cech cohomology for Nisnevich topology

I need the theorems that prove that Nisnevich cohomology can be computed by the Cech complex similar to what happens in the ├ętale topology. I know this has to be true since (Morel-Voevodsky: ...
14
votes
3answers
1k views

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 ...