CM cycles over Shimura Curves

This paper has now appeared in Journal of Algebraic Geometry, volume 4 659--693

Abstract: We look at a Shimura curve $X$ of discriminant $D$ and possibly some level structure and a universal family of Abelian surfaces with QM ${\cal A}\longrightarrow X$. We prove that the $r$-th Griffiths group of ${\cal A}^r$ (fibered product over $X$) has infinite rank. (this paper will appear on Journal of algebraic geometry)