Motives and representability of algebraic cycles on threefolds over a field
Motives and representability of algebraic cycles on threefolds over a field
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域上三次代数循环的动机和可表示性
DOI：
10.1090/s1056-3911-2011-00548-1
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发表时间：
2008
影响因子：
1.8
通讯作者：
V. Guletskiĭ
中科院分区：
文献类型：
--
作者：
S. Gorchinskiy;V. Guletskiĭ
我们研究了三重代数圈之间的联系，以及它们的动机的有限维性与Q中的系数。我们将具有CH_0（X）的可表示代数部分的非奇异投射三重X的动机分解为某个交换簇的Lefschetz动机和Picard动机，当基场为C时，这些交换簇与相应的中间Jacobian J^2（X）同构.特别是，它意味着一个域上的Fano三重的motivic有限维。我们还用代数H^2证明了几类三重纤维曲面上零圈的可表示性。这给出了动机是有限维的三维变体的另一个新例子。
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.