2022 Theses Doctoral

# Geometric pullback formula for unitary Shimura varieties

In this thesis we study Kudlaβs special cycles of codimension π on a unitary Shimura variety Sh(U(n β 1,1)) together with an embedding of a Shimura subvariety Sh(U(m β 1,1)). We prove that when π = π β π, for certain cuspidal automorphic representations π of the quasi-split unitary group U(π,π) and certain cusp forms β¨ β π, the geometric volume of the pullback of the arithmetic theta lift of β¨ equals the special value of the standard πΏ-function of π at π = (π β π + 1)/2. As ingredients of the proof, we also give an exposition of Kudlaβs geometric Siegel-Weil formula and Yuan-Zhang-Zhangβs pullback formula in the setting of unitary Shimura varieties, as well as Qinβs integral representation result for πΏ-functions of quasi-split unitary groups.

## Subjects

## Files

- Dung_columbia_0054D_17150.pdf application/pdf 411 KB Download File

## More About This Work

- Academic Units
- Mathematics
- Thesis Advisors
- Li, Chao
- Degree
- Ph.D., Columbia University
- Published Here
- April 20, 2022