Motives and representability of algebraic cycles on threefolds over a field

S. Gorchinskiy; V. Guletskii

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arXiv · 0806.0173

Motives and representability of algebraic cycles on threefolds over a field

S. Gorchinskiy·V. Guletskii

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Abstract

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 representability of zero-cycles on several classes of threefolds fibered by surfaces with algebraic H^2. This gives another new examples of three-dimensional varieties whose motives are finite-dimensional.

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BibTeX RIS

S. Gorchinskiy, V. Guletskii. 2008-06-01. Motives and representability of algebraic cycles on threefolds over a field. https://arxiv.org/abs/0806.0173

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