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Geometric Pullback Formula for Unitary Shimura Varieties.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Geometric Pullback Formula for Unitary Shimura Varieties./
Author:	Dung, Nguyễn Chi.
Description:	1 online resource (68 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 83-10, Section: B.
Contained By:	Dissertations Abstracts International83-10B.
Subject:	Mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798426811928

Geometric Pullback Formula for Unitary Shimura Varieties.
Dung, Nguyễn Chi.

Geometric Pullback Formula for Unitary Shimura Varieties. - 1 online resource (68 pages)

Source: Dissertations Abstracts International, Volume: 83-10, Section: B.

Thesis (Ph.D.)--Columbia University, 2022.

Includes bibliographical references

In this thesis we study Kudla's special cycles of codimension r on a unitary Shimura variety Sh(U(n − 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 f ∈ π, the geometric volume of the pullback of the arithmetic theta lift of f 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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798426811928Subjects--Topical Terms:

527692
Mathematics.
Subjects--Index Terms:

Arithmetic geometryIndex Terms--Genre/Form:

554714
Electronic books.

Geometric Pullback Formula for Unitary Shimura Varieties.
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500 $a Source: Dissertations Abstracts International, Volume: 83-10, Section: B.
500 $a Advisor: Li, Chao.
502 $a Thesis (Ph.D.)--Columbia University, 2022.
504 $a Includes bibliographical references
520 $a In this thesis we study Kudla's special cycles of codimension r on a unitary Shimura variety Sh(U(n − 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 f ∈ π, the geometric volume of the pullback of the arithmetic theta lift of f 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.
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538 $a Mode of access: World Wide Web
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653 $a Arithmetic geometry
653 $a Automorphic forms
653 $a Mathematics
653 $a Number theory
653 $a Shimura varieties
653 $a L-functions
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