The Tate Conjecture for Powers of Ordinary Cubic Fourfolds over Finite Fields
نویسنده
چکیده
Recently N. Levin proved the Tate conjecture for ordinary cubic fourfolds over finite fields. In this paper we prove the Tate conjecture for selfproducts of ordinary cubic fourfolds. Our proof is based on properties of so called polynomials of K3 type introduced by the author about a dozen years ago.
منابع مشابه
The Tate conjecture for cubic fourfolds over a finite field
If X/F is a smooth projective variety over a finite field F of characteristic p > 0 and X = X ⊗ F, there is a cycle class map CH(X)→ H et (X,Q`(i)) for ` 6= p from the Chow group of codimension i cycles on X to étale cohomology. The image of this map lies in the subspace of H et (X,Q`(i)) which is invariant under the natural Galois action. In [T3], Tate conjectures that, in fact, this subspace ...
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