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arXiv · 1907.04143

On the Tate and Standard Conjectures over Finite Fields

James S Milne
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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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James S Milne. 2019-07-09. On the Tate and Standard Conjectures over Finite Fields. https://arxiv.org/abs/1907.04143

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