Old and new motivic cycles on Abelian surfaces

Abstract

Collino \cite{colo} discovered indecomposable motivic cycles in the group $H^{2g-1}_{\mathcal M}(J(C),{\mathds Z}(g))$. In an earlier paper we described the construction of some new motivic cycles which can be viewed as a generalization of Collino's cycle when $g=2$. In this paper we show that our new cycles are in fact related to Collino's cycles of higher genus. On one hand this suggests that new cycles are hard to find. On the other, it suggests that the tools developed to study Collino's cycle can be applied to our cycles.