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.

arXiv comment13 pages, French, published version, abstract added in migration

Cited by in corpus (7)

• The Tate conjecture over finite fields (AIM talk)
• Intermediate extension of Chow motives of Abelian type
• Standard conjectures for abelian fourfolds
• Normalization in integral models of Shimura varieties of Hodge type
• Motivic complexes over finite fields and the ring of correspondences at the generic point
• Conservativity of realizations on motives of abelian type over finite fields
• Polarizations and Grothendieck's Standard Conjectures