The University of Arizona
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Modularity and Heights of CM cycles on Kuga-Sato varieties

Algebra and Number Theory Seminar

Modularity and Heights of CM cycles on Kuga-Sato varieties
Series: Algebra and Number Theory Seminar
Location: ONLINE
Presenter: Congling Qiu, Yale Univ.

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.