La conjecture de Tate entière pour les cubiques de dimension quatre

Abstract

AbstractWe prove the integral Tate conjecture for cycles of codimension$2$on smooth cubic fourfolds over an algebraic closure of a field finitely generated over its prime subfield and of characteristic different from$2$or$3$. The proof relies on the Tate conjecture with rational coefficients, proved in that setting by the first author, and on an argument of Voisin coming from complex geometry.