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Roots of weight of a characteristic polynomial of Frobenius

We are expected to solve a conjecture of the title. Reference is Jean-Pierre Serre — Propriétés conjecturales des groupes de Galois motiviques et des représentations l-adiques. Precisely; Conjecture A:...
Takahiro Matsuda's user avatar
1 vote
0 answers
270 views

Eilenberg-Steenrod cohomological theory versus Weil cohomological theory [closed]

Can someone enlighten me what is the difference between an Eilenberg-Steenrod cohomological theory ( See here, https://en.wikipedia.org/wiki/Eilenberg%E2%80%93Steenrod_axioms ), and a Weil ...
Angel65's user avatar
  • 595
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
24 votes
3 answers
4k views

Are there "motivic" proofs of Weil conjectures in special cases?

This is a question meant as a first step to get into reading more on Weil conjectures and standard conjectures. It is known that the standard conjectures on vanishing of cycles would imply the Weil ...
Anweshi's user avatar
  • 7,442
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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