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 H0(X,Hq+1(Z(q)D))=0 if X is unirational. For a surface X with pg=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.
On the Deligne-Beilinson cohomology sheaves / L. Barbieri VIale. - In: THE ANNALS OF K-THEORY. - ISSN 2379-1683. - 1:1(2016), pp. 3-17. [10.2140/akt.2016.1.3]
On the Deligne-Beilinson cohomology sheaves
L. Barbieri VIalePrimo
2016
Abstract
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 H0(X,Hq+1(Z(q)D))=0 if X is unirational. For a surface X with pg=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.
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