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http://arks.princeton.edu/ark:/88435/dsp012n49t486r
Title: | Harmonic Analysis on Local Systems on Graphs -- Towards a Gross-Zagier Formula on CM-cycles over Shimura Curves |
Authors: | Wen, Boya |
Advisors: | Zhang, Shou-Wu |
Contributors: | Mathematics Department |
Keywords: | Green's function Gross-Zagier formula Height pairing Local systems on Graphs |
Subjects: | Mathematics |
Issue Date: | 2022 |
Publisher: | Princeton, NJ : Princeton University |
Abstract: | In Part I of the thesis, we study harmonic analysis on local systems over graphs, and construct Green's functions explicitly. In Part II, we apply the results in Part I towards a Gross-Zagier formula for CM cycles over Shimura curves, which connects the global height pairing of special cycles in Kuga varieties over Shimura curves with the derivatives of the $L$-functions associated to weight-$2k$ modular forms. More precisely, we present a suitable choice of integral model of the CM cycles, and compute local intersections at primes where the quaternion algebra associated with the Shimura curve ramifies. |
URI: | http://arks.princeton.edu/ark:/88435/dsp012n49t486r |
Alternate format: | The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog: catalog.princeton.edu |
Type of Material: | Academic dissertations (Ph.D.) |
Language: | en |
Appears in Collections: | Mathematics |
Files in This Item:
File | Description | Size | Format | |
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Wen_princeton_0181D_14003.pdf | 577.38 kB | Adobe PDF | View/Download |
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