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Equivalence numérique et équivalence cohomologique pour les variétés abéliennes sur les corps finis

Laurent Clozel
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Abstract

In characteristic zero, it was proven a long time ago by D. Lieberman that cohomological and numerical equivalence coincide for cycles on abelian varieties. In this paper we show this to be true also in a somewhat technical sense for abelian varieties defined over a finite field. The technicality is that the result is valid for l-adic cohomology for primes l of non-zero density.

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Laurent Clozel. 1999-07-01. Equivalence numérique et équivalence cohomologique pour les variétés abéliennes sur les corps finis. https://arxiv.org/abs/math/9907203

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