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Indecomposable Higher Chow Cycles

Published online by Cambridge University Press:  20 November 2018

Kenichiro Kimura
Kenichiro Kimura*
Affiliation:
Institute of Mathematics, University of Tsukuba, Tsukuba, 305-8571, Japan e-mail: kimurak@tsukuba.ac.jp
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Abstract

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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 $C{{H}^{2}}\left( X,\,1 \right)$ can be lifted to an indecomposable element in $C{{H}^{3}}\left( {{X}_{K}},\,2 \right)$ 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 $\mathbb{Q}$ then the $\mathbb{Q}$-vector space of indecomposable cycles $CH_{ind}^{3}{{\left( {{X}_{\mathbb{C}}},\,2 \right)}_{\mathbb{Q}}}$ is infinite dimensional.

In the second part we give a new definition of the group of indecomposable cycles of $C{{H}^{3}}\left( X,\,2 \right)$ and give an example of non-torsion cycle in this group.

Keywords

14C2519D45
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 2 , 01 June 2005 , pp. 237 - 243
Copyright
Copyright © Canadian Mathematical Society 2005

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