Theses Doctoral

Geometric pullback formula for unitary Shimura varieties

Dung, Nguyen Chi

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


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More About This Work

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