MOTIVES AND REPRESENTABILITY OF ALGEBRAIC CYCLES ON THREEFOLDS OVER A FIELD

作者：Gorchinskiy Sergey^*; Guletskii Vladimir

来源：Journal of Algebraic Geometry, 2012, 21(2): 347-373.

We study 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 CH0(X) into Lefschetz motives and the Picard motive of a certain abelian variety, isogenous to the Griffiths%26apos; 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 fibred by surfaces with algebraic H-2. This gives new examples of three-dimensional varieties whose motives are finite-dimensional.

• 出版日期2012-4