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On the Tate and Standard Conjectures over Finite Fields (1907.04143v1)
Published 9 Jul 2019 in math.AG and math.NT
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.
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