Geometric pullback formula for unitary Shimura varieties

Description

In this thesis we study Kudla’s special cycles of codimension 𝑟 on a unitary Shimura variety Sh(U(𝑚 − 1,1)) together with an embedding of a Shimura subvariety Sh(U(𝑚 − 1,1)). We prove that when 𝑟 = 𝑛 − 𝑚, for certain cuspidal automorphic representations 𝜋 of the quasi-split unitary group U(𝑟,𝑟) and certain cusp forms ⨍ ∈ 𝜋, the geometric volume of the pullbackof the arithmetic theta lift of ⨍ equals the special value of the standard 𝐿-function of 𝜋 at 𝑠 = (𝑚 − 𝑟 + 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.

Links & Downloads

1. https://doi.org/10.7916/5k1m-ak45

Tags

Mathematics

Shimura varieties

Unitary groups

Additional Fields

Identifer	oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/5k1m-ak45
Date	January 2022
Creators	Dung, Nguyen Chi
Source Sets	Columbia University
Language	English
Detected Language	English
Type	Theses