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

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.