Algebraic Cycles and Motives: On the Splitting of the Bloch–Beilinson Filtration

@article{Beauville2004AlgebraicCA,
  title={Algebraic Cycles and Motives: On the Splitting of the Bloch–Beilinson Filtration},
  author={Arnaud Beauville},
  journal={arXiv: Algebraic Geometry},
  year={2004}
}
  • A. Beauville
  • Published 22 March 2004
  • Mathematics
  • arXiv: Algebraic Geometry
For a smooth projective variety X, let CH(X) be the Chow ring (with rational coefficients) of algebraic cycles modulo rational equivalence. The conjectures of Bloch and Beilinson predict the existence of a functorial ring filtration of CH(X). We want to investigate for which varieties this filtration splits, that is, comes from a graduation on CH(X) -- this occurs for K3 surfaces and, conjecturally, for abelian varieties. We observe that, though the Bloch-Beilinson filtration is only… 
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