Return to search

Geometric pullback formula for unitary Shimura varieties

In this thesis we study Kudla’s special cycles of codimension π‘Ÿ on a unitary Shimura variety Sh(U(π‘š βˆ’ 1,1)) together with an embedding of a Shimura subvariety Sh(U(π‘š 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 pullbackof 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.

Identiferoai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/5k1m-ak45
Date January 2022
CreatorsDung, Nguyen Chi
Source SetsColumbia University
LanguageEnglish
Detected LanguageEnglish
TypeTheses

Page generated in 0.0022 seconds