On the Deligne-Beilinson cohomology sheaves

We prove that the Deligne-Beilinson cohomology sheaves Hq+1 (Z(q)D) are torsion-free as a consequence of the Bloch-Kato conjectures as proven by Rost and Voevodsky. This implies that H-0(X, Hq+1 (Z(q)(D))) = 0 if X is unirational. For a surface X with p(g = 0) we show that the Albanese kernel, identified with H0 (X, H3 (Z(2)D)), can be characterized using the integral part of the sheaves associated to the Hodge filtration.