Zero-Cycles on Varieties Over Finite Fields

Abstract

Abstract We prove that for a smooth projective variety X of dimension d defined over a finite field k, the structure map σ : X → Spec k induces an isomorphism σ∗ : CH d+1(X, 1) ≅ CH 1(k, 1) = k*. We also prove that the higher Chow groups CH d+s−1(X, s) of one-dimensional cycles are torsion for s ≥ 2.