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6
votes
1answer
561 views

Motivic proof of Weil-conjectures?

Assuming the standard conjectures (and whatever is needed in addition), is there a nice proof of the Weil-conjectures written completely in the language of motives?
5
votes
0answers
145 views

Nice references for injective model structures and Quillen functors between motivic homotopy categories

It seems that for the injective model structures for the categories simplicial presheaves and simplicial Nisnevich sheaves (on the category of smooth varieties over a perfect field $k$) there exist ...
16
votes
1answer
643 views

For which varieties is the natural map from the Chow ring to integral cohomology an isomorphism?

My apologies if this question is too naive. Let $X$ be a smooth projective complex variety. There is a natural map $A^{\bullet}(X) \to H^{2\bullet}(X)$ of graded rings from the Chow ring of $X$ to ...