Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Motives and representability of algebraic cycles on threefolds over a field

Authors: Sergey Gorchinskiy and Vladimir Guletskiĭ
Journal: J. Algebraic Geom. 21 (2012), 347-373
Published electronically: May 31, 2011
Corrigendum: J. Algebraic Geom. 22 (2013), 795-796
MathSciNet review: 2877438
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Abstract | References | Additional Information

Abstract: We study algebraic cycles on threefolds and finite-dimensionality of their motives with coefficients in $ \mathbb{Q}$. We decompose the motive of a non-singular projective threefold $ X$ with representable algebraic part of $ CH_0(X)$ into Lefschetz motives and the Picard motive of a certain abelian variety, isogenous to the Griffiths' intermediate Jacobian $ J^2(X)$ when the ground field is $ \mathbb{C}$. In particular, it implies motivic finite-dimensionality of Fano threefolds over a field. We also prove representability of zero-cycles on several classes of threefolds fibred by surfaces with algebraic $ H^2$. This gives new examples of three-dimensional varieties whose motives are finite-dimensional.

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Sergey Gorchinskiy
Affiliation: Steklov Mathematical Institute, Gubkina str. 8, 119991, Moscow, Russia

Vladimir Guletskiĭ
Affiliation: Department of Mathematical Sciences, University of Liverpool, Peach Street, Liverpool L69 7ZL, England, United Kingdom

Received by editor(s): July 3, 2009
Received by editor(s) in revised form: September 21, 2009
Published electronically: May 31, 2011
Additional Notes: The first author was partially supported by the grants RFBR 08-01-00095, NSh-1987.2008.1 and MK-297.2009.1.

American Mathematical Society