Modularity and Heights of CM cycles on Kuga-Sato varieties
We study CM cycles on Kuga-Sato varieties over X(N). Our first result is the modularity of the unramified Hecke module generated by CM cycles. This result enable us to decompose the space of CM cycles according to the unramified Hecke action. Our second result is the full modularity of all CM cycles in the components of representations with vanishing central (base change) L-values. Finally, we prove a higher weight analog of the general Gross-Zagier formula of Yuan, S. Zhang and W. Zhang.