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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.
Alternate format: The Mudd Manuscript Library retains one bound copy of each dissertation. Search for these copies in the library's main catalog:
Type of Material: Academic dissertations (Ph.D.)
Language: en
Appears in Collections:Mathematics

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