15
$\begingroup$

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.

$\endgroup$

1 Answer 1

21
$\begingroup$

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

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