Resumen de Indecomposable Higher Chow Cycles

Kenichiro Kimura

• 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.