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Mathematische Annalen

, Volume 331, Issue 1, pp 173–201 | Cite as

Chow groups are finite dimensional, in some sense

  • Shun-Ichi KimuraEmail author
Article

Abstract.

When S is a surface with p g (S)>0, Mumford proved that its Chow group A*S is not “finite dimensional” in some sense. In this paper, we propose another definition of “finite dimensionality” for the Chow groups. Using this new definition, at least the Chow group of some surface S with p g (S)>0 (for example, the product of two curves) becomes finite dimensional. The finite dimensionality of the Chow groups follows from the finite dimensionality of the Chow motives. It turns out that the finite dimensionality of the Chow motives is a very strong property. For example, we can prove Bloch’s conjecture (representability of the Chow groups of surfaces with p g (S)=0) under the assumption that the Chow motive of S is finite dimensional.

Keywords

Strong Property Chow Group Finite Dimensionality Chow Motive 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsHiroshima UniversityHigashi-HiroshimaJapan

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