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摘要翻译：
本文研究了三重上的代数圈与其动因的有限维数与系数q之间的联系，将具有CH_0(X)可表示的代数部分的非奇异射影三重X的动因分解为Lefschetz动因和某一阿贝尔变体的Picard动因，当基场为C时，它与相应的中间雅可比J^2(X)等同。特别地，它蕴涵了场上Fano三重的动因有限维数。我们还证明了由代数H^2曲面构成的几类三重函数上零圈的可表示性。这给出了另一个动机是有限维的三维变体的新例子。
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英文标题：
《Motives and representability of algebraic cycles on threefolds over a
field》
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作者：
S. Gorchinskiy, V. Guletskii
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最新提交年份：
2012
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分类信息：
一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
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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PDF链接：
https://arxiv.org/pdf/0806.0173
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