Indecomposable Higher Chow Cycles

• Autores: Kenichiro Kimura
• Localización: Canadian mathematical bulletin, ISSN 0008-4395, Vol. 48, Nº 2, 2005, págs. 237-243
• Idioma: inglés
• DOI: 10.4153/cmb-2005-021-7
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• Resumen

  • Let X be a projective smooth variety over a field k. In the first part we show that an indecomposable element in CH2(X,1) can be lifted to an indecomposable element in CH3(XK,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 mathbb Q then the mathbb Q-vector space of indecomposable cycles CH3ind(Xmathbb C,2)mathbb Q is infinite dimensional. In the second part we give a new definition of the group of indecomposable cycles of CH3(X,2) and give an example of non-torsion cycle in this group.