Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

According to Weil, the Weil conjecture should follow once one has a sufficiently powerful cohomology machine. And it is proved using one of them, namely étale cohomology.

My question is, has there been any attempt, after its proof using étale cohomology, to prove it using other Weil cohomology theories? i.e. a cohomology theory which has finiteness, allow Poincaré duality, Künneth formula, cycle map, weak and strong Lefschetz. After all it is a motivic thing.

share|improve this question
add comment

1 Answer

Yes. See Kedlaya's Fourier transforms and p-adic Weil II. This is a proof using Berthelot's rigid cohomology.

share|improve this answer
add comment

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.