# Motives and representability of algebraic cycles on threefolds over a field

@article{Gorchinskiy2008MotivesAR, title={Motives and representability of algebraic cycles on threefolds over a field}, author={S. Gorchinskiy and V. Guletskiĭ}, journal={Journal of Algebraic Geometry}, year={2008}, volume={21}, pages={347-373} }

We study links between algebraic cycles on threefolds and finite-dimensionality of their motives with coefficients in 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 corresponding intermediate Jacobian J^2(X) when the ground field is C. In particular, it implies motivic finite-dimensionality of Fano threefolds over a field. We also prove…

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