Indecomposable Higher Chow Cycles

Abstract

AbstractLet 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 ℚ then the ℚ-vector space of indecomposable cycles 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.