Open Access
Translator Disclaimer
2016 On the Deligne–Beilinson cohomology sheaves
Luca Barbieri-Viale
Ann. K-Theory 1(1): 3-17 (2016). 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.

Citation

Download Citation

Luca Barbieri-Viale. "On the Deligne–Beilinson cohomology sheaves." Ann. K-Theory 1 (1) 3 - 17, 2016. https://doi.org/10.2140/akt.2016.1.3

Information

Received: 24 December 2014; Accepted: 30 December 2014; Published: 2016
First available in Project Euclid: 12 December 2017

zbMATH: 1346.14024
MathSciNet: MR3514934
Digital Object Identifier: 10.2140/akt.2016.1.3

Subjects:
Primary: 14C35
Secondary: 14C30 , 14F42

Keywords: $K$-theory , algebraic cycles , Hodge theory

Rights: Copyright © 2016 Mathematical Sciences Publishers

JOURNAL ARTICLE
15 PAGES


SHARE
Vol.1 • No. 1 • 2016
MSP
Back to Top