The Tate Conjecture for Powers of Ordinary Cubic Fourfolds Over Finite Fields

Abstract

Recently N. Levin (Comp. Math. 127 (2001), 1--21) proved the Tate conjecture for ordinary cubic fourfolds over finite fields. In this paper we prove the Tate conjecture for self-products of ordinary cubic fourfolds. Our proof is based on properties of so called polynomials of K3 type introduced by the author (Duke Math. J. 72 (1993), 65--83).

LaTeX2e, 12 pages