The main results of this thesis describe a relationship between two families of arithmetic divisors on an integral model of a
Shimura curve. The first family, studied by Kudla, Rapoport and Yang, parametrizes abelian surfaces with specified endomorphism structure. The second family is comprised of pullbacks of arithmetic cycles on integral models of Shimura varieties associated to unitary groups of signature (1,1). In
the thesis, we construct these families of cycles, and describe their relationship, which is expressed in terms of the ``Shimura lift", a classical tool in the theory of modular forms of half-integral weight. This relations can be viewed as further evidence for the modularity of generating series of arithmetic "special cycles" for
U(1,1), and fits broadly into Kudla's programme for unitary groups.
| Identifer | oai:union.ndltd.org:TORONTO/oai:tspace.library.utoronto.ca:1807/34874 |
| Date | 19 December 2012 |
| Creators | Sankaran, Siddarth |
| Contributors | Kudla, Stephen S. |
| Source Sets | University of Toronto |
| Language | en_ca |
| Detected Language | English |
| Type | Thesis |
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