Remark on Weil's conjectures
arXiv:1309.2551 · doi:10.1515/apam-2015-0052
Abstract
We introduce a cohomology theory for a class of projective varieties over a finite field coming from the canonical trace on a C*-algebra attached to the variety. Using the cohomology, we prove the rationality, functional equation and the Betti numbers conjectures for the zeta function of the variety.
to appear Advances Pure and Applied Mathematics, De Gruyter