Abstract
We give conditions to determine if a cycle is indecomposable in the higher Chow group \(\text {CH}^{r}(X,m;\mathbb {Q})\), for X a complex smooth projective variety. We show that the primitive part of topological invariant associated with an arithmetic normal function of a cycle is related to its decomposability.
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Notes
As noticed by the referee, this is the case for each fibre of \(i_{*}\xi \).
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The author would like to thank the referees for their helpful comments that improved this paper considerably.
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The author is supported by the Cátedras Conacyt program.
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Castillo, J.J.H. Indecomposable cycles and arithmetic normal functions. Bol. Soc. Mat. Mex. 24, 61–79 (2018). https://doi.org/10.1007/s40590-016-0146-2
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DOI: https://doi.org/10.1007/s40590-016-0146-2