On the Tate and Standard Conjectures over Finite Fields
arXiv:1907.04143
Abstract
For an abelian variety over a finite field, Clozel (1999) showed that l-homological equivalence coincides with numerical equivalence for infinitely many l, and the author (1999) gave a criterion for the Tate conjecture to follow from Tate's theorem on divisors. We generalize both statements to motives, and apply them to other varieties including K3 surfaces.
The pdf file on my webpage is more robust