Vol. 1, No. 1, 2016

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On the Deligne–Beilinson cohomology sheaves

Luca Barbieri-Viale

Vol. 1 (2016), No. 1, 3–17
DOI: 10.2140/akt.2016.1.3
Abstract

We prove that the Deligne–Beilinson cohomology sheaves q+1((q)D) are torsion-free as a consequence of the Bloch–Kato conjectures as proven by Rost and Voevodsky. This implies that H0(X,q+1((q)D)) = 0 if X is unirational. For a surface X with pg = 0 we show that the Albanese kernel, identified with H0(X,3((2)D)), can be characterized using the integral part of the sheaves associated to the Hodge filtration.

Keywords
$K$-theory, Hodge theory, algebraic cycles
Mathematical Subject Classification 2010
Primary: 14C35
Secondary: 14C30, 14F42
Milestones
Received: 24 December 2014
Accepted: 30 December 2014
Published: 31 July 2015
Authors
Luca Barbieri-Viale
Dipartimento di Matematica “F. Enriques”
Università degli Studi di Milano
Via C. Saldini, 50
20133 Milano
Italy