Nonvanishing of External Products for Higher Chow Groups

Details Nonvanishing of External Products for Higher Chow Groups Nonvanishing of External Products for Higher Chow Groups

2001-12-06

arxiv.org/abs/math/0112058v6

Mathematics

Algebraic Geometry

18 pages, some arguments in Sect. 3 are improved

Scientific paper

Consider an external product of a higher cycle and a usual cycle which is algebraically equivalent to zero. Assume there exists an algebraically closed subfield k such that the higher cycle and its ambient variety are defined over k, but the image of the usual cycle by the Abel-Jacobi map is not. Then we prove that the external product is nonzero if the image of the higher cycle by the cycle map to the reduced Deligne cohomology does not vanish. We also give examples of indecomposable higher cycles on even dimensional hypersurfaces of degree at least four in a projective space such that the last condition is satisfied.

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