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14 votes
2 answers
2k views

How would a motivic proof of the Riemann hypothesis over finite fields go?

It is well known that Grothendieck had a different idea than Deligne about how one should go about proving the Riemann hypothesis for finite fields. However, since Grothendieck's desired proof never ...
James D. Taylor's user avatar
8 votes
3 answers
3k views

Why is the zeta function of a variety over a finite field not a polynomial? (question about motives)

I've been doing some light(?) reading on motives and the standard conjectures in an attempt to put various things that I tangentially know in perspective. The question is this: the Weil conjectures ...
Makhalan Duff's user avatar
35 votes
4 answers
8k views

What would a "moral" proof of the Weil Conjectures require?

At the very end of this 2006 interview (rm), Kontsevich says "...many great theorems are originally proven but I think the proofs are not, kind of, "morally right." There should be better proofs......
bhwang's user avatar
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