# Joint IAS/Princeton University Number Theory Seminar

## Modularity and Heights of CM cycles on Kuga-Sato varieties

We study CM cycles on Kuga-Sato varieties over $X(N)$ via theta lifting and relative trace formula. Our first result is the modularity of CM cycles, in the sense that the Hecke modules they generate are semisimple whose irreducible components are associated to higher weight holomorphic cuspidal automorphic representations of $GL_2(Q)$. This is proved via theta lifting. Our second result is a higher weight analog of the general Gross-Zagier formula of Yuan, S. Zhang and W. Zhang. This is proved via relative trace formula, provided the modularity of CM cycles.

### Date & Time

October 14, 2021 | 4:30pm – 5:30pm

### Location

Fine Hall 214, Princeton University and Remote Access

Congling Qiu

Yale University

### Notes

Zoom link password hint: the three digit integer that is the cube of the sum of its digits.