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Indecomposable Higher Chow Cycles

Open Access article
 Printed: Jun 2005
  • Kenichiro Kimura
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Let $X$ be a projective smooth variety over a field $k$. In the first part we show that an indecomposable element in $CH^2(X,1)$ can be lifted to an indecomposable element in $CH^3(X_K,2)$ where $K$ is the function field of 1 variable over $k$. We also show that if $X$ is the self-product of an elliptic curve over $\Q$ then the $\Q$-vector space of indecomposable cycles $CH^3_{ind}(X_\C,2)_\Q$ is infinite dimensional. In the second part we give a new definition of the group of indecomposable cycles of $CH^3(X,2)$ and give an example of non-torsion cycle in this group.
MSC Classifications: 14C25, 19D45 show english descriptions Algebraic cycles
Higher symbols, Milnor $K$-theory
14C25 - Algebraic cycles
19D45 - Higher symbols, Milnor $K$-theory

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