Indecomposable Higher Chow Cycles

Kimura, Kenichiro

Canadian mathematical bulletin, Tome 48 (2005) no. 2, pp. 237-243

Résumé

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.

Détail

DOI : 10.4153/CMB-2005-021-7

Mots-clés : 14C25, 19D45